On Gödel incompleteness and finite combinatorics

DOI10.1016/0168-0072(87)90074-1zbMath0627.03041OpenAlexW2036673058MaRDI QIDQ581400

Akihiro Kanamori, Kenneth McAloon

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0168-0072(87)90074-1

zbMATH Keywords

partitioncombinatorial principleindependence of Peano Arithmetic

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Models of arithmetic and set theory (03C62)

Related Items (31)

Phase transition results for three Ramsey-like theorems ⋮ Unprovability of sharp versions of Friedman’s sine-principle ⋮ Regressive Partition Relations for Infinite Cardinals ⋮ Fragments of strong compactness, families of partitions and ideal extensions ⋮ Unnamed Item ⋮ THE STRENGTH OF RAMSEY’S THEOREM FOR COLORING RELATIVELY LARGE SETS ⋮ Regressive partitions and Borel diagonalization ⋮ A Combinatorial Approach to Complexity Theory via Ordinal Hierarchies ⋮ Sharp thresholds for hypergraph regressive Ramsey numbers ⋮ The Paris-Harrington principle and second-order arithmetic -- bridging the finite and infinite Ramsey theorem ⋮ A WALK WITH GOODSTEIN ⋮ Combinatorial principles concerning approximations of functions ⋮ Incompleteness Theorems, Large Cardinals, and Automata Over Finite Words ⋮ Incompleteness Theorems, Large Cardinals, and Automata over Finite Words ⋮ Combinatorial unprovability proofs and their model-theoretic counterparts ⋮ Regressive partition relations, \(n\)-subtle cardinals, and Borel diagonalization ⋮ Sharp thresholds for the phase transition between primitive recursive and Ackermannian Ramsey numbers ⋮ Fast growing functions based on Ramsey theorems ⋮ A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points ⋮ Relationship between Kanamori-McAloon Principle and Paris-Harrington Theorem ⋮ Regressive functions on pairs ⋮ Directed graphs and boron trees ⋮ The canonical Ramsey theorem and computability theory ⋮ An Unprovable Ramsey-Type Theorem ⋮ Unnamed Item ⋮ Partition Theorems and Computability Theory ⋮ CURRENT RESEARCH ON GÖDEL’S INCOMPLETENESS THEOREMS ⋮ Phase transitions for Gödel incompleteness ⋮ Regressive Ramsey numbers are Ackermannian ⋮ Analytic combinatorics, proof-theoretic ordinals, and phase transitions for independence results ⋮ On regressive Ramsey numbers

Cites Work

• Rapidly growing Ramsey functions
• On the complexity of models of arithmetic
• Accessible Independence Results for Peano Arithmetic
• Some independence results for Peano arithmetic
• Some strong axioms of infinity incompatible with the axiom of constructibility
• A Combinatorial Theorem
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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