A Note on Intended and Standard Models

Abstract

This note discusses some problems concerning intended, standard, and nonstandard models of mathematical theories. We pay attention to the role of extremal axioms in attempts at a unique characterization of the intended models. We recall also Jan Woleński’s views on these issues.

Keywords

• intended model
• standard model
• extremal axiom
• metalogic
• categoricity
• completeness
• jan woleński