Finite injury and Σ1-induction

DOI10.2307/2275013zbMath0671.03029OpenAlexW2233217370MaRDI QIDQ3824402

Michael E. Mytilinaios

Publication date: 1989

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2275013

zbMATH Keywords

blockingpriority argumentSacks splitting\(\Sigma _ 1\)-induction

Mathematics Subject Classification ID

Axiomatics of classical set theory and its fragments (03E30) Recursively (computably) enumerable sets and degrees (03D25) Computability and recursion theory (03D99)

Related Items

Iterated trees and fragments of arithmetic, Fragments of Kripke-Platek set theory and the metamathematics of \(\alpha \)-recursion theory, \(\Sigma_ 2\) induction and infinite injury priority arguments. II. Tame \(\Sigma_ 2\) coding and the jump operator, On recursion theory in IΣ₁, 1994–1995 Winter Meeting of the Association for Symbolic Logic, Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem, \(\varPi^1_1\)-conservation of combinatorial principles weaker than Ramsey's theorem for pairs, \(\Delta_{2}\) degrees without \(\Sigma_{1}\) induction, Maximal sets and fragments of Peano arithmetic, Subsystems of second-order arithmetic between \(\text{RCA}_{0}\) and \(\text{WKL}_{0}\), \(\Sigma_2\) induction and infinite injury priority arguments. III: Prompt sets, minimal pairs and Shoenfield's conjecture, The Role of True Finiteness in the Admissible Recursively Enumerable Degrees, The degree of a \(\Sigma_ n\) cut, THE THEORY OF THE METARECURSIVELY ENUMERABLE DEGREES, Hyperhypersimple sets and \(\Delta _ 2\) systems, \(\Sigma_2\)-constructions and \(\text{I}\Sigma_1\)

Cites Work

• On the degrees less than 0'
• TWO RECURSIVELY ENUMERABLE SETS OF INCOMPARABLE DEGREES OF UNSOLVABILITY (SOLUTION OF POST'S PROBLEM, 1944)
• The α-finite injury method
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