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.
Proof theoretic aspects of quasi-inductive definitions / Bruni, Riccardo. - STAMPA. - (2010), pp. 81-93. (Intervento presentato al convegno Conferenza Annuale SILFS).
Proof theoretic aspects of quasi-inductive definitions
BRUNI, RICCARDO
2010
Abstract
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.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.