Work

Borel sets without perfectly many overlapping translations, III

Year: 2025

Type: article

Abstract: We expand the results of Rosłanowski and Shelah [11] , [10] to all perfect Abelian Polish groups ( H , + ) . In particular, we show that if α < ω 1 and 4 ≤ k < ω , then there is a ccc forcing notion adding a Σ 2 0 set B ⊆ H which has ℵ α many pairwise k –overlapping translations but not a perfect set of such translations. The technicalities of the forcing construction led us to investigations of the question when, in an Abelian group, X − X ⊆ Y − Y imply that a translation of X or − X is included in Y .

Source: Annals of Pure and Applied Logic

DOI: 10.1016/j.apal.2025.103565

Authors: Andrzej Rosłanowski, Saharon Shelah

Institutions: University of Nebraska at Omaha, Rutgers, The State University of New Jersey, Hebrew University of Jerusalem

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

Funders: National Science Foundation, Israel Science Foundation