Work

Upwards Homogeneity in Iterated Symmetric Extensions

Year: 2025

Type: article

Abstract: It is sometimes desirable in choiceless constructions of set theory that one iteratively extends some ground model without adding new sets of ordinals after the first extension. Pushing this further, one may wish to have models $V\subseteq M\subseteq N$ of ${\mathsf {ZF}}$ such that N contains no subsets of V that do not already appear in M . We isolate, in the case that M and N are symmetric extensions (particular inner models of a generic extension of V ), the exact conditions that cause this behaviour and show how it can broadly be applied to many known constructions. We call this behaviour upwards homogeneity.

Source: Journal of Symbolic Logic

DOI: 10.1017/jsl.2025.10148

Authors: CALLIOPE RYAN-SMITH, JONATHAN SCHILHAN, YUJUN WEI

Institution: University of Leeds

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: UK Research and Innovation, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences