Two-cardinal Kurepa Hypotheses

2025/10/09 by Fei Wu, Wu, Fanxin
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2510.08860

openalex publication_date 2025/10/09 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

We consider the two-cardinal Kurepa Hypothesis KH(κ,λ). We observe that if κ≤λ<μ are infinite cardinals then \lnotKH(κ,λ)\landKH(κ,μ)\rightarrowKH(λ⁺,μ), and show that in some sense this is the only ZFC constraint. The case of singular λ and its relation to Chang's Conjecture and scales is discussed. We also extend an independence result about Kurepa and Aronszajn trees due to Cummings to the case of successors of singular cardinal.

Citations

• Two-cardinal ideal operators and indescribability
• The generalized Kurepa hypothesis at singular cardinals
• Independence of higher Kurepa hypotheses
• Some consequences of reflection on the approachability ideal

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• The generalized Kurepa hypothesis at singular cardinals
• Chang's conjecture may fail at supercompact cardinals (submitted)
• Independence of higher Kurepa hypotheses
• On the spectra of cardinalities of branches of Kurepa trees
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