Higher Solovay Models

2025/07/25 by Straffelini, Cesare, Thei, Sebastiano
#03E15 #03E35 #03E45 #03E55 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2507.19129

Abstract

We introduce an axiomatisation of when a model of the form L(V_κ+1)^M can be considered a ``κ-Solovay model''; we show a characterisation of κ-Solovay models; and we prove elementary equivalences between κ-Solovay models.

Citations

• Generalized Descriptive Set Theory at Singular Cardinals of Countable Cofinality
• Sigma-Prikry forcing II: Iteration Scheme
• I0 and rank-into-rank axioms
• Generalized Descriptive Set Theory and Classification Theory

Related

• Combinatorics in Higher Solovay Models
• Independence relations in the Solovay model I
• Perfect set dichotomy theorem in generalized Solovay model
• Translation procedures in descriptive inner model theory
• Definability and almost disjoint families