Year: 2025
Type: article
Abstract: We study versions of the tree pigeonhole principle, TT 1 $\mathsf {TT}^1$ sans serif upper T upper T Superscript 1 , in the context of Weihrauch-style computable analysis. The principle has previously been the subject of extensive research in reverse mathematics, an outstanding question of which investigation is whether TT 1 $\mathsf {TT}^1$ sans serif upper T upper T Superscript 1 is Π 1 1 $\Pi ^1_1$ normal upper Pi 1 Superscript 1 -conservative over the ordinary pigeonhole principle, RT 1 $\mathsf {RT}^1$ sans serif upper R upper T Superscript 1 . Using the recently introduced notion of the first-order part of an instance-solution problem, we formulate the analog of this question for Weihrauch reducibility, and give an affirmative answer. In combination with other results, we use this to show that unlike RT 1 $\mathsf {RT}^1$ sans serif upper R upper T Superscript 1 , the problem TT 1 $\mathsf {TT}^1$ sans serif upper T upper T Superscript 1 is not Weihrauch requivalent to any first-order problem. Our proofs develop new combinatorial machinery for constructing and understanding solutions to instances of TT 1 $\mathsf {TT}^1$ sans serif upper T upper T Superscript 1 .
Source: Journal of Symbolic Logic
DOI: 10.1017/jsl.2025.11
Institutions: University of Connecticut, University of Wisconsin–Madison
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
Funder: National Science Foundation
OpenAlex ID: W4407383728