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A RECURSIVE COLORING FUNCTION WITHOUT $ \Pi _3^0$ SOLUTIONS FOR HINDMAN’S THEOREM

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

Published online by Cambridge University Press:  29 October 2024

YUKE LIAO
YUKE LIAO*
Affiliation:
DEPARTMENT OF MATHEMATICS NATIONAL UNIVERSITY OF SINGAPORE SINGAPORE 119076
*
E-mail: liao_yuke@u.nus.edu
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Abstract

We show that there exists a recursive coloring function c such that any $\Pi ^0_3$ set is not a solution to c for Hindman’s theorem. We also show that there exists a recursive coloring function c such that any $\Delta ^0_3$ set is not a solution to c for Hindman’s theorem restricted to sums of at most three numbers.

Keywords

reverse mathematicsHindman’s theorem

MSC classification

Primary: 03B30: Foundations of classical theories (including reverse mathematics) 03F35: Second- and higher-order arithmetic and fragments 03D80: Applications of computability and recursion theory

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Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 24
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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