A generalized small model property for languages which force the infinity

TL;DR

This paper introduces a technique to determine satisfiability of set theory formulas that enforce infinity, by reducing the problem to finite assignments, advancing understanding of models in infinite set theories.

Contribution

It presents a generalized small model property for languages that force infinity, enabling finite reasoning about infinite set-theoretic formulas.

Findings

Finite assignments can determine satisfiability of formulas forcing infinity

The technique simplifies reasoning in infinite set theories

Advances the theoretical understanding of small model properties

Abstract

This paper deals with formulas of set theory which force the infinity. For such formulas, we provide a technique to infer satisfiability from a finite assignment.