Higher Solovay Models

TL;DR

This paper introduces an axiomatisation and characterisation of $ abla$-Solovay models, providing elementary equivalences and a formal framework for understanding these models in set theory.

Contribution

It offers a new axiomatisation and characterisation of $ abla$-Solovay models, advancing the theoretical understanding of these models in set theory.

Findings

Axiomatisation of $ abla$-Solovay models

Characterisation of $ abla$-Solovay models

Elementary equivalences between $ abla$-Solovay models

Abstract

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