Independence relations in the Solovay model I

TL;DR

This paper introduces a new geometric axiomatization of the Solovay model, enabling simpler proofs of classical results and facilitating a geometric approach to the theory of balanced forcing.

Contribution

It provides a novel geometric framework for the Solovay model, simplifying proofs and advancing the understanding of forcing in set theory.

Findings

A new geometric axiomatization of the Solovay model

Forcing-free proofs of classical results

Development of a geometric theory of balanced forcing

Abstract

I provide a novel geometric axiomatization of the Solovay model. This serves as a vehicle for concise and forcing-free proofs of classical results in the model, as well as a tool for a purely geometric development of the theory of balanced forcing.