Phase transition thresholds for some Friedman-style independence results

Mathematical Logic Quarterly 53 (1):4-18 (2007)
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Abstract

We classify the phase transition thresholds from provability to unprovability for certain Friedman-style miniaturizations of Kruskal's Theorem and Higman's Lemma. In addition we prove a new and unexpected phase transition result for ε0. Motivated by renormalization and universality issues from statistical physics we finally state a universality hypothesis

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10.1002/malq.200610022

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Citations of this work

Current Research on Gödel’s Incompleteness Theorems.Yong Cheng - 2021 - Bulletin of Symbolic Logic 27 (2):113-167.
Phase transitions for Gödel incompleteness.Andreas Weiermann - 2009 - Annals of Pure and Applied Logic 157 (2-3):281-296.

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References found in this work

Proof-theoretic investigations on Kruskal's theorem.Michael Rathjen & Andreas Weiermann - 1993 - Annals of Pure and Applied Logic 60 (1):49-88.
On the interpretation of non-finitist proofs–Part II.G. Kreisel - 1952 - Journal of Symbolic Logic 17 (1):43-58.

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