Predicative foundations of arithmetic
The aim of the paper is to show that a predicatively acceptable axiomatization of the natural number system can be formulated and that the existence of the appropriate structures as well as the categoricity of the axioms can be proved in a predicatively acceptable way. A three- sorted system EFSC (elementary theory of finite sets and classes) and an extension of EFSC are constructed and studied. It is shown that EFSC contains Peano arithmetic PA and is a conservative extension of PA.
elementary theory of finite sets and classes
predicatively acceptable axiomatization of the natural number system
scientific article; zbMATH DE number 724110