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Phase transitions for Gödel incompleteness

Andreas Weiermann
2009 Annals of Pure and Applied Logic  
For these independence principles we classify (as a part of a general research program) their phase transitions, i.e. we classify exactly the bounding conditions which lead from provability to unprovability  ...  As Gödel numbering for ordinals we choose the one which is induced naturally from Gödel's coding of finite sequences from his classical 1931 paper on his incompleteness results.  ...  The author also thanks the John Templeton foundation for supporting generously his phase transition project via the ''Exploring the infinite initiative''.  ... 
doi:10.1016/j.apal.2008.09.012 fatcat:qdcffliq2zanll6nbfsfn3j67y

Phase transitions in logic and combinatorics

Andreas Weiermann
2005 Expositions of Current Mathematics  
We try to explain our intuition about the nature of phase transition results under discussion.  ...  The resulting phase transitions from provability to unprovability are interesting from the foundational as well as from the mathematical point of view.  ...  Phase transitions and Gödel incompleteness The phase transition phenomenon is familiar from statistical physics, [8] , but also from percolation [17] , random graphs [3, 19] and computational complexity  ... 
doi:10.11429/emath1996.2005.autumn-meeting1_42 fatcat:qb4jb2l7dng3vpqjt75rre2fci

Logical Approaches to Computational Barriers: CiE 2006

A. Beckmann, B. Lowe, D. Normann
2007 Journal of Logic and Computation  
Soskova 546 Table of Contents XV Phase Transition Thresholds for Some Natural Subclasses of the Computable Functions Andreas Weiermann 556 Kurt Gödel and Computability Theory Richard Zach  ...  XII Table of Contents of Gödel and the Origins of Computer ScienceJohn W.  ... 
doi:10.1093/logcom/exm031 fatcat:lv36duerfvd25inr2f2be56qvq

Logical Analysis of Hybrid Systems [chapter]

André Platzer
2012 Lecture Notes in Computer Science  
T 2.2 Incompleteness of dL . . . . . . . . . . . . . . . . . . . . . . . . . T 2.3 Relative completeness of dL . . . . . . . . . . . . . . . . . . . . .  ...  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 ETCS transition structure and various choices of speed regulation for train speed control . . . . . . . . . . . . . . . . . . . . . . . .  ... 
doi:10.1007/978-3-642-31623-4_3 fatcat:b7gnxodcqfgsfgj7an4aiptazm

Psychoanalytic Process: the Paradoxes of Self-Reference and Intermediacy

Alan Bass
2010 Konturen  
Freud does not account for the transition between the "friendly" and terrifying aspects of uncanniness.  ...  incompleteness has some version of self-referential paradoxicality lurking around in the background" (Goldstein, p. 165, n.5) .  ... 
doi:10.5399/uo/konturen.3.1.1401 fatcat:ewe26rp7ebho7iy4xdkser3r3u

The boundary of Gödel's spacetime and the chronology protection conjecture [article]

P. Pitanga
2012 arXiv   pre-print
Acknowledgments I am grateful to S.Deser, S.Jofilly, L.Ryff, K.Mundim, A.Antunes, C.Sigaud, C.Farina and J.Koiller for discussions, and to Marcela Gonçalves for encouragements.  ...  transition from trivial to non-trivial topology mediated by a first order (continuous) phase transition at the edge of the horizons.  ...  For our purpose it is sufficient to analyze the (2+1)-dimensional Gödel spacetime manifold with constant angular velocity ω 0 , and negative cosmological constant Λ.  ... 
arXiv:1201.1129v2 fatcat:65dyarl4gjgg7lj37xn6h43pva

Page 1775 of Mathematical Reviews Vol. , Issue 85e [page]

1985 Mathematical Reviews  
From the text: “The Boltzmann medal for 1983 is awarded to Michael Fisher for his many illuminating contributions to phase transitions and critical phenomena during the past 25 years.” 85e:01044  ...  During this discussion, Gédel briefly men- tioned his recently obtained (but still unpublished) incompleteness results.  ... 


2018 Horizon: Fenomenologičeskie Issledovaniâ  
This is the case, for instance, for Weyl and Gödel himself, even if both of them gradually abandoned phenomenology for, respectively, constructivism/predicativism and Platonism.  ...  Although this latter is widespread among mathematicians, a few of them still think that the continuum conjecture is relevant for a philosophical foundation of set theory and, in general, for a scientific  ...  Among others, this is the case for J. Klein, H. Weyl, and K. Gödel.  ... 
doi:10.21638/2226-5260-2018-7-1-137-159 fatcat:3zhi4634xbc7xoeyrfwc7qtj2e

The Genius of Alan Turing: The Computing Classical Model

Luís Homem
2013 International Journal of Machine Learning and Computing  
There are some variations in the model of a Turing machine, for example where one slides only to the right or ones possessing 5-tuple transitions basic states, instead of the classical 4-tuple transitions  ...  We aim to trace back the constituent phases of this convolution, by presenting at last a panoptical and functional plane of the computus realization, which has, by the passage from incompleteness to effective  ... 
doi:10.7763/ijmlc.2013.v3.364 fatcat:6igb3yknsjb4nggq2klmtotdnq

Turing oracle machines, online computing, and three displacements in computability theory

Robert I. Soare
2009 Annals of Pure and Applied Logic  
to "incomplete."  ...  Define an oracle program P i as follows with transition function δ : Q × S 1 × S 2 −→ Q × S 2 × {R, L}, for S 1 = {B, 0, 1} the oracle tape alphabet as follows.  ... 
doi:10.1016/j.apal.2009.01.008 fatcat:66vngrvfhfcr3c2rq36p2pbaeq

Page 2285 of Mathematical Reviews Vol. , Issue 86f [page]

1986 Mathematical Reviews  
Team, Oslo, 1983; MR 84k:03047a], the argument presented by Godel in the introduction to his 1931 incompleteness paper was translated into B-mathematics.  ...  This point is illustrated with a discussion of hyperfinite statistical mechanics along with applications to the classical Ising model and phase transitions; free Euclidean fields are a further illustration  ... 

Nut Charged Space-times and Closed Timelike Curves on the Boundary

Dumitru Astefanesei, Robert B Mann, Eugen Radu
2005 Journal of High Energy Physics  
Misner string analysis for general k We consider here the question of Misner string singularities for compactified Taub-NUT-AdS spacetimes.  ...  for k = 1 but not for k = 0 (in this case there is a phase transition if one considers the AdS soliton instead of AdS [50] ).  ...  That is, there is a phase transition between k = 1 Taub-Bolt-AdS and Taub-NUT-AdS.  ... 
doi:10.1088/1126-6708/2005/01/049 fatcat:rle6hjmif5fkdbkjh67hfuhmzu

Bernays and the Completeness Theorem

Walter DEAN
2017 Annals of the Japan Association for Philosophy of Science  
Just prior to their presentation of Gödel's Incompleteness Theorem, Hilbert and Bernays describe the significance of this form of his Completeness Theorem as follows: The transition from the formula F  ...  This yields a method for constructing counter-models for formulas falsifiable in a finite domain which Gödel showed could be extended to arbitrary formulas.  ... 
doi:10.4288/jafpos.25.0_45 fatcat:hdjy6zyp2ra7vlr4pwr4bg52fe

Metaphysics and mathematics: Perspectives on reality

Gideon J. Kühn
2017 HTS Teologiese Studies/Theological Studies  
The formalist approach to establish mathematical proof was found to be inconclusive: Gödel showed that there existed true propositions that could not be proved to be true within the natural number universe  ...  This result weighed heavily on proposals in the mid-20th century for digital models of the universe, inspired by the emergence of the programmable digital computer, giving rise to the branch of philosophy  ...  The technology is at present in an exploratory phase with realisation of a full-scale quantum computer somewhere in the future. not suffer the Gödel incompleteness properties.  ... 
doi:10.4102/hts.v73i3.4663 fatcat:hkwtblrdi5aafmak6xyss3e2bq

Undecidability everywhere? [article]

Karl Svozil
1995 arXiv   pre-print
Gödel [22] as well as Turing [62] used "the liar" [5] for their incompleteness theorems. Gödel was well aware of the fact that almost any classical paradox might do as well.  ...  Gödel, for instance, proved his incompleteness theorems as he succeeded to properly code a (generic) theory about arithmetic within arithmetic.  ... 
arXiv:chao-dyn/9509023v1 fatcat:ry6wpfvwtbe3doztha3k4gchfm
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