Generalized Tukey reducibility between σ-directed sets

2025/07/09 by Hiroshi Sakai, Sakai, Hiroshi, Toshimasa Tanno +1
Mathematics · Computer Science · #Advanced Topology and Set Theory #Advanced Banach Space Theory #Computability, Logic, AI Algorithms

paper · pdf · doi:10.48550/arxiv.2507.07309

Abstract

We introduce the pre-Tukey reducibility, a generalization of the Tukey reducibility between directed sets that works well in ZF. We investigate the pre-Tukey reducibility between several σ-directed sets under assumptions on sets of reals, which hold in the Solovay model and in L(ℝ) satisfying AD.

Citations

• Hechler's theorem for the meager ideal

Related

• Directed Sets of Topology -- Tukey Representation and Rejection
• On embedding certain partial orders into the P-points under RK and Tukey reducibility
• Tukey reduction among analytic directed orders
• Cofinal types on ω₂
• Survey on the Tukey theory of ultrafilters