Phase transitions for Gödel incompleteness

DOI10.1016/j.apal.2008.09.012zbMath1165.03048OpenAlexW2003007940MaRDI QIDQ1006619

Andreas Weiermann

Publication date: 25 March 2009

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2008.09.012

zbMATH Keywords

phase transitionsasymptotic behaviourprovabilityanalytic combinatoricsunprovabilityTauberian theoryproof-theoretic ordinalsFriedman-style independence resultsGödel incompleteness

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Asymptotic enumeration (05A16) Recursive ordinals and ordinal notations (03F15) Gödel numberings and issues of incompleteness (03F40)

Related Items (6)

Proof Theory in Philosophy of Mathematics ⋮ Hyperations, Veblen progressions and transfinite iteration of ordinal functions ⋮ Unprovability threshold for the planar graph minor theorem ⋮ Phase transitions of iterated Higman-style well-partial-orderings ⋮ Pure \(\Sigma_2\)-elementarity beyond the core ⋮ A Glimpse of $$ \sum_{3} $$-elementarity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Gödel incompleteness and finite combinatorics
• Sharp thresholds for the phase transition between primitive recursive and Ackermannian Ramsey numbers
• Classifying the phase transition threshold for Ackermannian functions
• Elementary descent recursion and proof theory
• Dynamic ordinal analysis
• Slow versus fast growing
• Asymptotics of Mahler recurrences: The cyclotomic case
• The strength of infinitary Ramseyan principles can be accessed by their densities
• More on lower bounds for partitioning \(\alpha\)-large sets
• Analytic combinatorics, proof-theoretic ordinals, and phase transitions for independence results
• The number of trees
• A century of complex Tauberian theory
• An extremely sharp phase transition threshold for the slow growing hierarchy
• Phase transition thresholds for some Friedman-style independence results
• Classifying the Provably Total Functions of PA
• GROWTH OF FINITELY GENERATED POLYNILPOTENT LIE ALGEBRAS AND GROUPS, GENERALIZED PARTITIONS, AND FUNCTIONS ANALYTIC IN THE UNIT CIRCLE
• Partition Functions Whose Logarithms are Slowly Oscillating
• Accessible Independence Results for Peano Arithmetic
• Some independence results for Peano arithmetic
• Percolation
• A classification of rapidly growing Ramsey functions
• An application of graphical enumeration to PA *
• Determining computational complexity from characteristic ‘phase transitions’
• A Sharp Phase Transition Threshold for Elementary Descent Recursive Functions
• Combinatorial Theorems on Classifications of Subsets of a Given Set
• Logical Approaches to Computational Barriers

This page was built for publication: Phase transitions for Gödel incompleteness