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RELATIVE LEFTMOST PATH PRINCIPLES AND OMEGA-MODEL REFLECTIONS OF TRANSFINITE INDUCTIONS

Part of: Computability and recursion theory Proof theory and constructive mathematics General logic

Published online by Cambridge University Press:  09 June 2025

YUDAI SUZUKI Open the ORCID record for YUDAI SUZUKI [Opens in a new window]
YUDAI SUZUKI*
Affiliation:
NATIONAL INSTITUTE OF TECHNOLOGY OYAMA JAPAN
*
E-mail: yudai.suzuki.research@gmail.com
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Abstract

In this article, we give characterizations of Towsner’s relative leftmost path principles in terms of omega-model reflections of transfinite inductions. In particular, we show that the omega-model reflection of $\Pi ^1_{n+1}$ transfinite induction is equivalent to the $\Sigma ^0_n$ relative leftmost path principle over $\mathsf {RCA}_0$ for $n> 1$. As a consequence, we have that $\Sigma ^0_{n+1}\mathsf {LPP}$ is strictly stronger than $\Sigma ^0_{n}\mathsf {LPP}$.

Keywords

reverse mathematicssecond-order arithmeticrelative leftmost path principleomega-model reflectionWeihrauch degrees

MSC classification

Primary: 03B30: Foundations of classical theories (including reverse mathematics) 03D30: Other degrees and reducibilities 03D55: Hierarchies 03F35: Second- and higher-order arithmetic and fragments

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Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 15
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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