Peano's Axioms and Models of Arithmetic

Abstract

The chapter discusses Peano's axioms and models of arithmetic and presents, how models of a similar kind can be set up in a perfectly constructive way when some very restricted arithmetical theories are considered. The chapter also presents remarks on the setting up of models of certain fragments of number theory—in particular, fragments of recursive arithmetic. In these simple cases the definition of nonstandard models are established in a perfectly constructive way.