# Adding proof objects and inductive definition mechanisms to frege structures

Invited Paper

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## Abstract

A constructive theory RPT (Reflective Proof Theory) of proofs which has the following three features is introduced. (1) Proofs as objects. (2) Hierarchies of propositions and truths. (3) The mechanisms of inductive definitions of predicates. Three kinds of structures called Frege structures with inductively defined predicates, Frege structures with proof objects and proof structures are also introduced. These structures are obtained by generalizing certain aspects of RPT and they are all closely related to Frege structures.

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© Springer-Verlag Berlin Heidelberg 1991