An arithmetical view to first-order logic

Abstract

A value space is a topological algebra B equipped with a non-empty family of continuous quantifiers ▪ : B ∗ → B . We will describe first-order logic on the basis of B . Operations of B are used as connectives and its relations are used to define statements. We prove under some normality conditions on the value space that any theory in the new setting can be represented by a classical first-order theory.