IA Scholar Query: Collapsing Exact Arithmetic Hierarchies.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgTue, 22 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440On ω-Strongly Measurable Cardinals
https://scholar.archive.org/work/edsxc3gv3nfmfdxdeu5xvlchse
We prove several consistency results concerning the notion of ω-strongly measurable cardinal in HOD. In particular, we show that is it consistent, relative to a large cardinal hypothesis weaker than o(κ) = κ, that every successor of a regular cardinal is ω-strongly measurable in HOD.Omer Ben-Neria, Yair Hayutwork_edsxc3gv3nfmfdxdeu5xvlchseTue, 22 Nov 2022 00:00:00 GMTMesh-free hydrodynamics in PKDGRAV3 for galaxy formation simulations
https://scholar.archive.org/work/n6esnbeq35eczg4ucdumyqdyaq
We extend the state-of-the-art N-body code PKDGRAV3 with the inclusion of mesh-free gas hydrodynamics for cosmological simulations. Two new hydrodynamic solvers have been implemented, the mesh-less finite volume and mesh-less finite mass methods. The solvers manifestly conserve mass, momentum and energy, and have been validated with a wide range of standard test simulations, including cosmological simulations. We also describe improvements to PKDGRAV3 that have been implemented for performing hydrodynamic simulations. These changes have been made with efficiency and modularity in mind, and provide a solid base for the implementation of the required modules for galaxy formation and evolution physics and future porting to GPUs. The code is released in a public repository, together with the documentation and all the test simulations presented in this work.Isaac Alonso Asensio, Claudio Dalla Vecchia, Douglas Potter, Joachim Stadelwork_n6esnbeq35eczg4ucdumyqdyaqTue, 22 Nov 2022 00:00:00 GMTSpecial Issue: Ludomaterialities
https://scholar.archive.org/work/mzj2yc7oqrhvhjsxatjw7nrqim
Spiele lassen sich nicht auf abstrakte Regelwerke oder narrative Strukturen reduzieren. Sie existieren in und gehen aus unterschiedlichen materiellen Spielkulturen hervor. Sie werden unter Einsatz von Ressourcen und Arbeit designt und produziert, sie benötigen Spielbretter, Würfel oder elektronische Interfaces und sie interagieren mit den Körpern der Spieler:innen ebenso wie mit den sie umgebenden Räumen. Das erste englischsprachige Special Issue der Spiel|Formen untersucht Ludomaterialitäten, d.h. die materiellen Korrelate von Spielen und spielerischen Praktiken, aus einer interdisziplinären Perspektive. Es ist ein Beitrag zum wachsenden Feld der Material Game Studies, das Forschungen zu Themen von Körperlichkeit und Materialität im Kontext von Spielen bündelt. Die Ausgabe ergänzt Übersetzungen bereits publizierter deutschsprachiger Artikel um neue Beiträge und Perspektiven und trägt so dazu bei, den deutschen Game Studies Diskurs an den im angloamerikanischen Raum proklamierten "Material Turn" anschlussfähig zu machen. Mit den gesammelten Beiträgen fokussiert der Band die Bereiche Design und Fanproduktion, Interfaceforschung, Geräte- und Datenverwertung, Medienpädagogik und Kunstgeschichte, adressiert dabei gleichzeitig aber auch explizit analoge Spielgeräte. Die Spannungen zwischen Material, Form und Regeln sowie zwischen Arbeit und Spiel sind zentrale Themen, die sich durch das Heft ziehen.(:Unkn) Unknown, Mediarep.Org, GamesCoopwork_mzj2yc7oqrhvhjsxatjw7nrqimMon, 21 Nov 2022 00:00:00 GMTHigh-Level Modelling and Solving for Online, Real-Time, and Multiagent Combinatorial Optimisation
https://scholar.archive.org/work/irdhjuvvuvfgnist333kkjl2am
This thesis presents a novel framework for declarative modelling and continual solving of dynamic combinatorial problems (e.g., planning the routes of delivery vehicles). This framework is then enhanced with a garbage collection mechanism, ensuring that the evolving problem's internal representation remains small as time progresses. Experiments show that garbage collection vastly improves runtime. This thesis presents another novel framework allowing experimentation with fairness in similar problems, which we show can achieve remarkably fair and resource-efficient solutions. Finally, this thesis presents one novel constraint propagation algorithm for variance and one for the Gini coefficient, which we show improve runtime.ALEXANDER JOHAN PHILIPPE EKwork_irdhjuvvuvfgnist333kkjl2amSun, 20 Nov 2022 00:00:00 GMT1st International Congress on Human Rights & Duties (The Rights, Vol-1: Issue-II, 10, December, 2015)
https://scholar.archive.org/work/cfn42bmtendmralrk7b4elusnq
1st International Congress on Human Rights & Duties (The Rights, Vol-1: Issue-II, 10, December, 2015)Yadam Research Institutework_cfn42bmtendmralrk7b4elusnqWed, 16 Nov 2022 00:00:00 GMTDagstuhl Reports, Volume 12, Issue 3, March 2022, Complete Issue
https://scholar.archive.org/work/atzdjkohs5hsdlk3uxxlt2ydry
Dagstuhl Reports, Volume 12, Issue 3, March 2022, Complete Issuework_atzdjkohs5hsdlk3uxxlt2ydryMon, 14 Nov 2022 00:00:00 GMTOn complex roots of the independence polynomial
https://scholar.archive.org/work/gmk3yhnacrfmxi7saztzrrqjre
It is known from the work of Shearer (1985) (and also Scott and Sokal (2005)) that the independence polynomial Z_G(λ) of a graph G of maximum degree at most d+1 does not vanish provided that |λ|≤d^d/(d+1)^d+1. Significant extensions of this result have recently been given in the case λ≥ 0 by Peters and Regts (2019) and Bencs and Csikvári (arxiv:1807.08963). In this paper, our motivation is to further extend these results and find zero free regions when λ≤ 0. We begin by giving new geometric criteria for establishing zero-free regions as well as for carrying out semi-rigorous numerical explorations. We then provide two examples of the (rigorous) use of these criteria, by establishing two new zero-free regions in the left-half plane. We also improve upon the results of Bencs and Csikvári (arxiv:1807.08963) for the right half-plane using our framework. By a direct application of the interpolation method of Barvinok, combined with extensions due to Patel and Regts, these results also imply deterministic polynomial time approximation algorithms for the independence polynomial of bounded degree graphs in the new zero-free regions.Ferenc Bencs, Péter Csikvári, Piyush Srivastava, Jan Vondrákwork_gmk3yhnacrfmxi7saztzrrqjreSun, 13 Nov 2022 00:00:00 GMTThe LDBC Social Network Benchmark
https://scholar.archive.org/work/n5ffojhw2faijg2aboolkmdirq
The Linked Data Benchmark Council's Social Network Benchmark (LDBC SNB) is an effort intended to test various functionalities of systems used for graph-like data management. For this, LDBC SNB uses the recognizable scenario of operating a social network, characterized by its graph-shaped data. LDBC SNB consists of two workloads that focus on different functionalities: the Interactive workload (interactive transactional queries) and the Business Intelligence workload (analytical queries). This document contains the definition of both workloads. This includes a detailed explanation of the data used in the LDBC SNB, a detailed description for all queries, and instructions on how to generate the data and run the benchmark with the provided software.Renzo Angles, János Benjamin Antal, Alex Averbuch, Altan Birler, Peter Boncz, Márton Búr, Orri Erling, Andrey Gubichev, Vlad Haprian, Moritz Kaufmann, Josep Lluís Larriba Pey, Norbert Martínez, József Marton, Marcus Paradies, Minh-Duc Pham, Arnau Prat-Pérez, Mirko Spasić, Benjamin A. Steer, Dávid Szakállas, Gábor Szárnyas, Jack Waudby, Mingxi Wu, Yuchen Zhangwork_n5ffojhw2faijg2aboolkmdirqWed, 09 Nov 2022 00:00:00 GMTIntelligent Bio-Latticed Cryptography: A Quantum-Proof Efficient Proposal
https://scholar.archive.org/work/pxzsopfdbjcihbnjtdrha6atxa
The emergence of the Internet of Things (IoT) and the tactile internet presents high-quality connectivity strengthened by next-generation networking to cover a vast array of smart systems. Quantum computing is another powerful enabler of the next technological revolution, which will improve the world tremendously, and it will continue to grow to cover an extensive array of important functions, in addition to it receiving recently great interest in the scientific scene. Because quantum computers have the potential to overcome various issues related to traditional computing, major worldwide technical corporations are investing competitively in them. However, along with its novel potential, quantum computing is introducing threats to cybersecurity algorithms, as quantum computers are able to decipher many complex mathematical problems that classical computers cannot. This research paper proposes a robust and performance-effective lattice-driven cryptosystem in the context of face recognition that provides lightweight intelligent bio-latticed cryptography, which will aid in overcoming the cybersecurity challenges of smart world applications in the pre- and post-quantum era and with sixth-generation (6G) networks. Since facial features are symmetrically used to generate encryption keys on the fly without sending or storing private data, our proposal has the valuable attribute of dramatically combining symmetric and asymmetric cryptography operations in the proposed cryptosystem. Implementation-based evaluation results prove that the proposed protocol maintains high-performance in the context of delay, energy consumption, throughput and stability on cellular network topology in classical Narrowband-Internet of Things (NB-IoT) mode.Ohood Saud Althobaiti, Toktam Mahmoodi, Mischa Dohlerwork_pxzsopfdbjcihbnjtdrha6atxaTue, 08 Nov 2022 00:00:00 GMTNearly optimal independence oracle algorithms for edge estimation in hypergraphs
https://scholar.archive.org/work/cod5s6nvoben7bu6hhympuxzhe
We study a query model of computation in which an n-vertex k-hypergraph can be accessed only via its independence oracle or via its colourful independence oracle, and each oracle query may incur a cost depending on the size of the query. In each of these models, we obtain oracle algorithms to approximately count the hypergraph's edges, and we unconditionally prove that no oracle algorithm for this problem can have significantly smaller worst-case oracle cost than our algorithms.Holger Dell and John Lapinskas and Kitty Meekswork_cod5s6nvoben7bu6hhympuxzheMon, 07 Nov 2022 00:00:00 GMTGene prioritization based on random walks with restarts and absorbing states, to define gene sets regulating drug pharmacodynamics from single-cell analyses
https://scholar.archive.org/work/vs3kzjm36nbq7ljmpxngfjhlmq
Prioritizing genes for their role in drug sensitivity, is an important step in understanding drugs mechanisms of action and discovering new molecular targets for co-treatment. To formalize this problem, we consider two sets of genes X and P respectively composing the gene signature of cell sensitivity at the drug IC50 and the genes involved in its mechanism of action, as well as a protein interaction network (PPIN) containing the products of X and P as nodes. We introduce Genetrank, a method to prioritize the genes in X for their likelihood to regulate the genes in P. Genetrank uses asymmetric random walks with restarts, absorbing states, and a suitable renormalization scheme. Using novel so-called saturation indices, we show that the conjunction of absorbing states and renormalization yields an exploration of the PPIN which is much more progressive than that afforded by random walks with restarts only. Using MINT as underlying network, we apply Genetrank to a predictive gene signature of cancer cells sensitivity to tumor-necrosis-factor-related apoptosis-inducing ligand (TRAIL), performed in single-cells. Our ranking provides biological insights on drug sensitivity and a gene set considerably enriched in genes regulating TRAIL pharmacodynamics when compared to the most significant differentially expressed genes obtained from a statistical analysis framework alone. We also introduce gene expression radars, a visualization tool embedded in MA plots to assess all pairwise interactions at a glance on graphical representations of transcriptomics data. Genetrank is made available in the Structural Bioinformatics Library (https://sbl.inria.fr/doc/Genetrank-user-manual.html). It should prove useful for mining gene sets in conjunction with a signaling pathway, whenever other approaches yield relatively large sets of genes.Augusto Sales de Queiroz, Guilherme Sales Santa Cruz, Alain Jean-Marie, Dorian Mazauric, Jérémie Roux, Frédéric Cazalswork_vs3kzjm36nbq7ljmpxngfjhlmqMon, 07 Nov 2022 00:00:00 GMTSoliton gas in integrable dispersive hydrodynamics
https://scholar.archive.org/work/6m5umm7gdjd23a3ylrfl4jac7a
We review spectral theory of soliton gases in integrable dispersive hydrodynamic systems. We first present a phenomenological approach based on the consideration of phase shifts in pairwise soliton collisions and leading to the kinetic equation for a non-equilibrium soliton gas. Then a more detailed theory is presented in which soliton gas dynamics are modelled by a thermodynamic type limit of modulated finite-gap spectral solutions of the Korteweg-de Vries and the focusing nonlinear Schr\"odinger equations. For the focusing nonlinear Schr\"odinger equation the notions of soliton condensate and breather gas are introduced that are related to the phenomena of spontaneous modulational instability and the rogue wave formation. Integrability properties of the kinetic equation for soliton gas are discussed and some physically relevant solutions are presented and compared with direct numerical simulations of dispersive hydrodynamic systems.Gennady A. Elwork_6m5umm7gdjd23a3ylrfl4jac7aSat, 05 Nov 2022 00:00:00 GMTAdvanced Automatic Code Generation for Multiple Relaxation-Time Lattice Boltzmann Methods
https://scholar.archive.org/work/bgi6sphh6jc6jopoaerxfqqnvy
The scientific code generation package lbmpy supports the automated design and the efficient implementation of lattice Boltzmann methods (LBMs) through metaprogramming. It is based on a new, concise calculus for describing multiple relaxation-time LBMs, including techniques that enable the numerically advantageous subtraction of the constant background component from the populations. These techniques are generalized to a wide range of collision spaces and equilibrium distributions. The article contains an overview of lbmpy's front-end and its code generation pipeline, which implements the new LBM calculus by means of symbolic formula manipulation tools and object-oriented programming. The generated codes have only a minimal number of arithmetic operations. Their automatic derivation rests on two novel Chimera transforms that have been specifically developed for efficiently computing raw and central moments. Information contained in the symbolic representation of the methods is further exploited in a customized sequence of algebraic simplifications, further reducing computational cost. When combined, these algebraic transformations lead to concise and compact numerical kernels. Specifically, with these optimizations, the advanced central moment- and cumulant-based methods can be realized with only little additional cost as when compared with the simple BGK method. The effectiveness and flexibility of the new lbmpy code generation system is demonstrated in simulating Taylor-Green vortex decay and the automatic derivation of an LBM algorithm to solve the shallow water equations.Frederik Hennig, Markus Holzer, Ulrich Rüdework_bgi6sphh6jc6jopoaerxfqqnvyFri, 04 Nov 2022 00:00:00 GMTJudgment Day 6: Details on planetary neurogenesis and clues in pyramids
https://scholar.archive.org/work/ya7n56ujz5cjff6hnsteni7uzu
In the analysis of the Solar System in context of Complete Relativity, a planetary neurogenesis has been hypothesized and discussed in light of evidence provided. Here, the 6th major event of neurogenesis on Earth is discussed, correlated with ancient prophecies, religions and pyramids in Giza, Egypt.Mario Ljubičićwork_ya7n56ujz5cjff6hnsteni7uzuWed, 02 Nov 2022 00:00:00 GMTSubjectivist Propaganda
https://scholar.archive.org/work/hstit4ods5fvvl6l7t2tv46rem
Physicalism is the default position in science and in the philosophy of mind, but it should not be, I argue, because of two errors. By its epistemological error, physicalism gives physics priority over the evidence of first person experience. Only what I experience in first person is certain, so observation is prior to any theory. Physics itself is based on observation, avoiding the epistemological error, and then physics can progress, even changing its own ontology. However, physicalism imposes the ontology of physics on every science, and in physics everything is causal. By its ontological error, physicalism tries to explain causally what is intentional. And it happens that causality and intentionality are mutually exclusive, showing that the ontology of physics is insufficient wherever intentions are present. This ontological insufficiency prevents that physicalism can repeat the success of physics with any science where intentions play a rôle, and thus it is blocking the advance of both the social sciences and the philosophy of mind. To overcome this obstacle, I propose to go back to the essentials: we should consider again the transcendental problem raised by Descartes and its solutions by Hume and Kant. On top of this subjectivist solution, we should take advantage of Darwin and Turing, and we should extend our ontology beyond causality to include intentionality, and here my proposal is problem solving. Then you could join our Post-Kantian subjectivism and say with me: The world is not a huge machine, as physicalism proposes, but an enigmatic problem.Ramón Casareswork_hstit4ods5fvvl6l7t2tv46remTue, 01 Nov 2022 00:00:00 GMTAn evaluation of the dominant assumptions and practices of training packages in Australian Vocational Education and Training and the extent to which they coincide with the emergence of mode-2 society and its imputed education and training needs
https://scholar.archive.org/work/3nhfjrmvb5cpri5khdvqc77bea
This research investigates the relevance of contemporary Australian Vocational Education and Training (VET) to economic development in Mode-2 society. Mode-2 society is a term coined by Nowotny et al (2001) which equates with changes in productivity and the triumph of free-market capitalism commonly referred to as knowledge driven capitalism or knowledge capitalism. Building on Schumpeter's economic theory of entrepreneurial competition and Romer's new growth economic model that have transformed capitalism into 'gales of creative destruction' by which new knowledge now generates national economic advantage, the thesis examines the literature of Training Packages as the prescribed instruments of VET in the milieu of knowledge capitalism. It could be expected that Australian VET, and in particular Training Packages, would have a greater justification for pursuing a knowledge and skill application-and-transfer policy that fits the growth of knowledge capitalism which Mode-2 society represents than it had for the former manufacturing economy. To test this contention, the thesis establishes eleven key transitions from Mode-1 to Mode-2 society and the imputed education and training needs of the latter as derived from the Nowotny et al (2001) Mode-2 thesis. These transitions are formed into an Evaluative Framework and underpin an ethnographic study involving thirty-three VET experts. The literature search and ethnography responses are synthesized and analysed with new material elicited from the ethnography. The outcomes of the analysis are equated with the eleven key transitions from Mode-1 to Mode-2 society and the imputed emergent education and training needs of each transition. It is concluded that the dominant assumptions and practices of Training Packages do not align with the imputed education and training needs of Mode-2 society as indicated by the eleven key attributes of the Nowotny et al (2001) conceptualisation. The theoretical implications of this conclusion had an impact on the Australian provision of VET b [...]Clive Grahamwork_3nhfjrmvb5cpri5khdvqc77beaFri, 28 Oct 2022 00:00:00 GMTNew Pipes, Old Ways: Water Infrastructure Failure, Power, and the State in Nigeria
https://scholar.archive.org/work/lr7hmtkrmzbedmgwa2xbqlh4lq
Repeated malfunction and failure of water supply infrastructure pose a critical challenge to equitable and sustainable water access, and the attainment of Sustainable Development Goals in most African countries. As part of the broader water governance problems, this challenge concerns the design and organisation of the distributive systems of water infrastructure. A governing approach that ignores power and historical relations in water infrastructure management presents interesting conceptual, theoretical, and practical problems. With Nigeria as a case study, this thesis seeks to understand some of these problems by asking the question: What are the changing effects of power on the development and governance of water infrastructure in Nigeria, and to what extent is it responsible for infrastructure failure? The thesis explores ideational, symbolic, and disciplinary power to examine this question through the Nigerian state using the Transaqua interbasin water transfer project and the Iganna water supply scheme in Oyo State, Nigeria. Through a focus on the logic of resistance, the thesis argues that water infrastructure failure and inequity in Nigeria are historically produced by political knowledge (e.g., policies and theories) and discursive practices (e.g., ideas and ideologies) at different water infrastructure and governance levels. The thesis revisits theoretical concepts like the hydraulic mission, and practical concepts like infrastructure renovation because of their ability to misrepresent contextual relations of power, or to mask and perpetuate inequitable water access and distribution. The Nigerian case shows the different motivations for state-making beyond the traditional arguments on spatial or autocratic control by the federal government, helps explain some contributing determinations of other water-related issues beyond the traditional analytical tropes of corruption, fragmentation, ethnicization, and allows us to question other analytical concepts in the political economy field that fundamentally [...]Adegboyega Adeniran, University, The Australian Nationalwork_lr7hmtkrmzbedmgwa2xbqlh4lqTue, 25 Oct 2022 00:00:00 GMTEfficient and Scalable Parallel Functional Programming Through Disentanglement
https://scholar.archive.org/work/obcpiwdvhfaszemjsojjttth24
Researchers have argued for decades that functional programming simplifies parallel programming, in particular by helping programmers avoid dificult concurrency bugs arising from destructive in-place updates. However, parallel functional programs have historically underperformed in comparison to parallel programs written in lower-level languages. The dificulty is that functional languages have high demand for memory, and this demand only grows with parallelism, causing traditional parallel memory management techniques to buckle under the increased pressure. In this thesis, we identify a memory property called disentanglement and develop automatic memory management techniques which exploit disentanglement for improved eficiency and scalability. Disentanglement has broad applicability: (1) it can be guaranteed by construction in functional programs; (2) it is implied by determinacy-race-freedom, a classic correctness condition; and (3) it allows for general reads and writes to memory as long as concurrent threads do not acquire references to each other's allocated data. Additionally, entanglement (i.e., violations of disentanglement) can be detected dynamically during program execution with nearly zero overhead in practice. To exploit disentanglement for improved efficiency, we partition memory into a tree of heaps, mirroring the dynamic nesting of parallel tasks, which allows for allocations and garbage collections to proceed independently and in parallel. We develop multiple garbage collection algorithms in this setting. There are two significant implementation efforts presented in this thesis. The first is the MPL ("maple") compiler for Parallel ML, which extends the Standard ML functional programming language with support for (nested) fork-join parallelism. In MPL, we implement all of our memory management techniques based on disentanglement. The second is the Parallel ML Benchmark Suite, which provides implementations of sophisticated parallel algorithms for a variety of problem domains, port [...]Samuel Westrickwork_obcpiwdvhfaszemjsojjttth24Mon, 24 Oct 2022 00:00:00 GMTOn Vacuum Structures and Quantum Corrections in String Theory
https://scholar.archive.org/work/26gtp4n6enfwlklbnlwofhzady
A key target for fundamental physics remains developing a clear understanding of ultra-violet (UV) limits of Effective Field Theories (EFTs) coupled to gravity. In this context, string theory has emerged as a viable candidate for a UV complete theory of quantum gravity. Its compactifications result in a landscape of string vacua encompassing an immensely rich and diverse structure of EFTs. Extracting reliable low energy information from string compactifications notoriously requires a systematic derivation of corrections to the tree level actions which remains a key challenge. Further, despite astonishing progress in constructing string solutions, locating realistic string vacua with desirable properties in the landscape proves to be a delicate task. The objectives of this thesis are threefold: I) first, to perform an extensive analysis of quantum corrections in string theory; II) second, to create a systematic framework to study geometries and backgrounds for viable string compactifications; and III) third, to assess the attainable EFTs in the context of moduli stabilisa- tion. The synergy of these strategies constitutes an innovative approach towards addressing phenomenological questions in string theory. The first part of this thesis describes progress in deriving corrections to classi- cal string effective actions from multi-dimensional investigations by employing the powerful machinery of string dualities and symmetries. Initially, we investigate the structure of higher derivative terms involving the 3-form G3 in the α′ and string-loop expansion of the ten-dimensional Type IIB effective action. Subsequently, we ex- plore α′ corrections in F-theory compactifications to four dimensions in Ch. 6. Here, we focus on the moduli dependence of perturbative corrections to scalar potentials by performing a dimensional analysis. The second part concerns the development of new techniques to examine large classes of Calabi-Yau (CY) geometries and realising the Standard Model in string compactifications. In a first step, w [...]Andreas Schachner, Apollo-University Of Cambridge Repository, Fernando Quevedowork_26gtp4n6enfwlklbnlwofhzadyFri, 21 Oct 2022 00:00:00 GMTAbsolute model companionship, forcibility, and the continuum problem
https://scholar.archive.org/work/7do2zhlvhvewnhzirjhqtbsxku
Absolute model companionship (AMC) is a strict strengthening of model companionship defined as follows: For a theory T, T_∃∨∀ denotes the logical consequences of T which are boolean combinations of universal sentences. T^* is the AMC of T if it is model complete and T_∃∨∀=T^*_∃∨∀. We use AMC to study the continuum problem and to gauge the expressive power of forcing. We show that (a definable version of) 2^ℵ_0=ℵ_2 is the unique solution to the continuum problem which can be in the AMC of a "partial Morleyization" of the ∈-theory 𝖹𝖥𝖢+"there are class many supercompact cardinals". We also show that (assuming large cardinals) forcibility overlaps with the apparently weaker notion of consistency for any mathematical problem ψ expressible as a Π_2-sentence of a (very large fragment of) third order arithmetic (𝖢𝖧, the Suslin hypothesis, the Whitehead conjecture for free groups are a small sample of such problems ψ). Partial Morleyizations can be described as follows: let 𝖥𝗈𝗋𝗆_τ be the set of first order τ-formulae; for A⊆𝖥𝗈𝗋𝗆_τ, τ_A is the expansion of τ adding atomic relation symbols R_ϕ for all formulae ϕ in A and T_τ,A is the τ_A-theory asserting that each τ-formula ϕ(x⃗)∈ A is logically equivalent to the corresponding atomic formula R_ϕ(x⃗). For a τ-theory T T+T_τ,A is the partial Morleyization of T induced by A⊆𝖥𝗈𝗋𝗆_τ. Finally we characterize a strong form of Woodin's axiom (*) as the assertion that the first order theory of H_ℵ_2 as formalized in a certain natural signature is model complete.Matteo Vialework_7do2zhlvhvewnhzirjhqtbsxkuFri, 21 Oct 2022 00:00:00 GMT