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Phase transitions for Gödel incompleteness

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''. ...

##
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Phase transitions in logic and combinatorics

2005
*
Expositions of Current Mathematics
*

We try to explain our intuition about the nature of

doi:10.11429/emath1996.2005.autumn-meeting1_42
fatcat:qb4jb2l7dng3vpqjt75rre2fci
*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 ...##
###
Logical Approaches to Computational Barriers: CiE 2006

2007
*
Journal of Logic and Computation
*

Soskova
546
Table of Contents
XV

doi:10.1093/logcom/exm031
fatcat:lv36duerfvd25inr2f2be56qvq
*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. ...##
###
Logical Analysis of Hybrid Systems
[chapter]

2012
*
Lecture Notes in Computer Science
*

T 2.2

doi:10.1007/978-3-642-31623-4_3
fatcat:b7gnxodcqfgsfgj7an4aiptazm
*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 . . . . . . . . . . . . . . . . . . . . . . . . ...##
###
Psychoanalytic Process: the Paradoxes of Self-Reference and Intermediacy

2010
*
Konturen
*

Freud does not account

doi:10.5399/uo/konturen.3.1.1401
fatcat:ewe26rp7ebho7iy4xdkser3r3u
*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) . ...##
###
The boundary of Gödel's spacetime and the chronology protection conjecture
[article]

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

arXiv:1201.1129v2
fatcat:65dyarl4gjgg7lj37xn6h43pva
*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. ...##
###
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. ...##
###
RETHINKING SPATIOTEMPORAL EXTENSION: HUSSERL'S CONTRIBUTION TO THE DEBATE ON THE CONTINUUM HYPOTHESIS

2018
*
Horizon: Fenomenologičeskie Issledovaniâ
*

This is the case,

doi:10.21638/2226-5260-2018-7-1-137-159
fatcat:3zhi4634xbc7xoeyrfwc7qtj2e
*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*. ...##
###
The Genius of Alan Turing: The Computing Classical Model

2013
*
International Journal of Machine Learning and Computing
*

There are some variations in the model of a Turing machine,

doi:10.7763/ijmlc.2013.v3.364
fatcat:6igb3yknsjb4nggq2klmtotdnq
*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 ...##
###
Turing oracle machines, online computing, and three displacements in computability theory

2009
*
Annals of Pure and Applied Logic
*

to "

doi:10.1016/j.apal.2009.01.008
fatcat:66vngrvfhfcr3c2rq36p2pbaeq
*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. ...##
###
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

2005
*
Journal of High Energy Physics
*

Misner string analysis

doi:10.1088/1126-6708/2005/01/049
fatcat:rle6hjmif5fkdbkjh67hfuhmzu
*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. ...##
###
Bernays and the Completeness Theorem

2017
*
Annals of the Japan Association for Philosophy of Science
*

Just prior to their presentation of Gödel's

doi:10.4288/jafpos.25.0_45
fatcat:hdjy6zyp2ra7vlr4pwr4bg52fe
*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. ...##
###
Metaphysics and mathematics: Perspectives on reality

2017
*
HTS Teologiese Studies/Theological Studies
*

The formalist approach to establish mathematical proof was found to be inconclusive:

doi:10.4102/hts.v73i3.4663
fatcat:hkwtblrdi5aafmak6xyss3e2bq
*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. ...##
###
Undecidability everywhere?
[article]

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. ...

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