Work

MA ( I ) and a failure of separation on the third level

Year: 2025

Type: article

Abstract: We present a method which forces the failure of Π 3 1 and Σ 3 1 -separation, while MA ( I ) holds, for I the family of indestructible ccc forcings. This shows that, in contrast to the assumption BPFA and ℵ 1 = ℵ 1 L which implies Π 3 1 -separation, that weaker forcing axioms do not decide separation on the third projective level.

Source: Annals of Pure and Applied Logic

DOI: 10.1016/j.apal.2025.103667

Author: Stefan Hoffelner

Institution: TU Wien

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,520

Funder: Austrian Science Fund