Switch to: References

Citations of:

The Consistency Strengths of Some Finite Forms of the Higman and Kruskal Theorems

Rick L. Smith

Journal of Symbolic Logic 55 (2):869-870 (1990)

Add citations

You must login to add citations.

Analytic combinatorics, proof-theoretic ordinals, and phase transitions for independence results.Andreas Weiermann - 2005 - Annals of Pure and Applied Logic 136 (1):189-218.details This paper is intended to give for a general mathematical audience a survey of intriguing connections between analytic combinatorics and logic. We define the ordinals below ε0 in non-logical terms and we survey a selection of recent results about the analytic combinatorics of these ordinals. Using a versatile and flexible compression technique we give applications to phase transitions for independence results, Hilbert’s basis theorem, local number theory, Ramsey theory, Hydra games, and Goodstein sequences. We discuss briefly universality and renormalization issues (...) Download Export citation Bookmark 11 citations
A comparison of well-known ordinal notation systems for ε0.Gyesik Lee - 2007 - Annals of Pure and Applied Logic 147 (1):48-70.details We consider five ordinal notation systems of ε0 which are all well-known and of interest in proof-theoretic analysis of Peano arithmetic: Cantor’s system, systems based on binary trees and on countable tree-ordinals, and the systems due to Schütte and Simpson, and to Beklemishev. The main point of this paper is to demonstrate that the systems except the system based on binary trees are equivalent as structured systems, in spite of the fact that they have their origins in different views and (...) Download Export citation Bookmark 1 citation
A Uniform Approach to Fundamental Sequences and Hierarchies.Wilfried Buchholz, Adam Cichon & Andreas Weiermann - 1994 - Mathematical Logic Quarterly 40 (2):273-286.details In this article we give a unifying approach to the theory of fundamental sequences and their related Hardy hierarchies of number-theoretic functions and we show the equivalence of the new approach with the classical one. Download Export citation Bookmark 23 citations
Phase transitions for Gödel incompleteness.Andreas Weiermann - 2009 - Annals of Pure and Applied Logic 157 (2-3):281-296.details Gödel’s first incompleteness result from 1931 states that there are true assertions about the natural numbers which do not follow from the Peano axioms. Since 1931 many researchers have been looking for natural examples of such assertions and breakthroughs were obtained in the seventies by Jeff Paris [Some independence results for Peano arithmetic. J. Symbolic Logic 43 725–731] , Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977] and Laurie Kirby [L. Kirby, Jeff Paris, Accessible independence results for Peano Arithmetic, Bull. of (...) Download Export citation Bookmark 5 citations

1