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An axiomatic approach to symmetric extensions

Peter Holy
Vol. 340 (2026), No. 2, 293–307
DOI: 10.2140/pjm.2026.340.293
Abstract

We provide a collection of natural axioms centered around the symmetric forcing theorem, which yield the concept of symmetric extensions, avoiding the technicalities involved in standard presentations.

Keywords
forcing, symmetric extension
Mathematical Subject Classification
Primary: 03E40, 03E30, 03E25, 03A05
Milestones
Received: 8 November 2024
Revised: 23 September 2025
Accepted: 23 September 2025
Published: 26 November 2025
Authors
Peter Holy
Institut für Diskrete Mathematik und Geometrie
TU Wien
1040 Wien
Austria
© 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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