Proof theoretic aspects of quasi-inductive definitions
Riccardo Bruni · Florence Research (University of Florence) · 2010
I introduce a new family of theories which axiomatizes the denition clauses and the basic properties of quasi{inductive de- nitions (see [2]). Further, I provide some initial proof{theoretic result. Namely, it is shown that theories for iterated (monotone) inductive denitions ID can be interpreted in the theory for arithmetical quasi{ inductive denition from the family of theories I present. In turn, this latter system of axioms is similarly proved to be embeddable into a modication of Kripke-Platek set theory, augmented with a strong reflection assumption.