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On the strength of Ramsey's theorem without Σ1 -induction
Mathematical Logic Quarterly 59 (1-2):108-111 (2013)
Abstract
In this paper, we show that equation image is a equation image-conservative extension of BΣ1 + exp, thus it does not imply IΣ1My notes
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Citations of this work
Reverse mathematics and Peano categoricity.Stephen G. Simpson & Keita Yokoyama - 2013 - Annals of Pure and Applied Logic 164 (3):284-293.
Weaker cousins of Ramsey's theorem over a weak base theory.Marta Fiori-Carones, Leszek Aleksander Kołodziejczyk & Katarzyna W. Kowalik - 2021 - Annals of Pure and Applied Logic 172 (10):103028.
On principles between ∑1- and ∑2-induction, and monotone enumerations.Alexander P. Kreuzer & Keita Yokoyama - 2016 - Journal of Mathematical Logic 16 (1):1650004.
How Strong is Ramsey’s Theorem If Infinity Can Be Weak?Leszek Aleksander Kołodziejczyk, Katarzyna W. Kowalik & Keita Yokoyama - 2023 - Journal of Symbolic Logic 88 (2):620-639.
Reverse mathematics, young diagrams, and the ascending chain condition.Kostas Hatzikiriakou & Stephen G. Simpson - 2017 - Journal of Symbolic Logic 82 (2):576-589.
References found in this work
On the strength of Ramsey's theorem for pairs.Peter A. Cholak, Carl G. Jockusch & Theodore A. Slaman - 2001 - Journal of Symbolic Logic 66 (1):1-55.
Factorization of polynomials and °1 induction.S. G. Simpson - 1986 - Annals of Pure and Applied Logic 31:289.
Reverse mathematics and Peano categoricity.Stephen G. Simpson & Keita Yokoyama - 2013 - Annals of Pure and Applied Logic 164 (3):284-293.
Some independence results for peano arithmetic.J. B. Paris - 1978 - Journal of Symbolic Logic 43 (4):725-731.
On the strength of Ramsey's theorem for pairs.Peter A. Cholak, Carl G. Jockusch & Theodore A. Slaman - 2001 - Journal of Symbolic Logic 66 (1):1-55.
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