Some independence results related to finite trees-Reference-Cited by-同舟云学术

Some independence results related to finite trees

Published:2023-04-10 Issue:2248 Volume:381 Page:
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Friedman Harvey M.¹,Weiermann Andreas²^ORCID

Affiliation:

1. Department of Mathematics, Ohio State University, Mathematics Building, 231 West 18th Avenue, Columbus, OH 43210, USA

2. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Krijgslaan 281 S8, 9000 Ghent, Belgium

Abstract

We investigate some concrete independence results for systems of reverse mathematics which emerge from monotonicity properties of number-theoretic functions. Natural properties of the less than or equal to relation with respect to sums of natural numbers lead to independence results for first-order Peano arithmetic. Natural properties of the less than or equal to relation with respect to sums and products of natural numbers lead to independence results for arithmetical transfinite recursion. By considering number-theoretic functions of arbitrary arities, we obtain independence results for systems beyond arithmetical transfinite recursion. We discuss how these embeddability relations are related to tree embeddability relations and we consider variants where the tree embeddability relation is not assumed to preserve infima. The findings of this paper are complementary to results on Kruskal-like theorems proved earlier by the first author. This article is part of the theme issue ‘Modern perspectives in Proof Theory’.

Funder

Fonds Wetenschappelijk Onderzoek

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2022.0017

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1. On the logical strength of the better quasi order with three elements;Transactions of the American Mathematical Society;2023-06-21

2. Modern perspectives in Proof Theory;Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences;2023-04-10