Higher Solovay Models

Abstract

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

28 pages; minor corrections in v2