Work

On semiproperness of Namba forcings and ideals in Prikry extensions

Year: 2025

Type: article

Abstract: We study some variations of Namba forcing Nm(κ,λ) over Pκλ and show that its semiproperness implies SSR([λ]ω,<κ). In particular, Prikry forcing at μ forces that Namba forcing Nm(μ+) is not semiproper. This shows that there are no semiproper saturated ideals in extensions by Prikry-type forcings. We also show that [λ+]μ+ cannot carry a λ+-saturated semiproper ideal if μ is singular with countable cofinality.

Source: Fundamenta Mathematicae

DOI: 10.4064/fm231119-23-6

Author: Kenta Tsukuura

Institution: National Fisheries University

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: Strong, Japan Society for the Promotion of Science

Award: Study of anti-compactness of saturated ideals