Universal properties of truth

TL;DR

This paper explores the model theoretic properties related to definability of truth predicates in formal languages, analyzing conditions and axioms that ensure such definability and their interrelations.

Contribution

It introduces new axiomatic frameworks and characterizes when truth predicates are definable in models, advancing understanding of truth in formal systems.

Findings

Identifies conditions for truth predicate definability

Formulates axiomatic theories for truth properties

Analyzes mutual definability relations between theories

Abstract

We investigate abstract model theoretic properties which holds for models in which a truth or satisfaction predicate for a sublanguage of the signature is definable. We analyse in which cases those properties in fact ensure the definability of the respective truth predicate. In some cases, we formulate different axiomatic theories which are indispensable for such properties to hold and we analyse the mutual definability relations between those theories.