This paper introduces theories for arithmetical quasi-inductive definitions (Burgess, 1986) as it has been done for first-order monotone and nonmonotone inductive ones. After displaying the basic axiomatic framework, we provide some initial result in the proof theoretic bounds line of research (the upper one being given in terms of a theory of sets extending Kripke–Platek set theory).
A Note on Theories for Quasi-Inductive Definitions / Bruni, Riccardo. - In: THE REVIEW OF SYMBOLIC LOGIC. - ISSN 1755-0203. - STAMPA. - 2:(2009), pp. 684-699. [10.1017/S175502030909025X]
A Note on Theories for Quasi-Inductive Definitions
BRUNI, RICCARDO
2009
Abstract
This paper introduces theories for arithmetical quasi-inductive definitions (Burgess, 1986) as it has been done for first-order monotone and nonmonotone inductive ones. After displaying the basic axiomatic framework, we provide some initial result in the proof theoretic bounds line of research (the upper one being given in terms of a theory of sets extending Kripke–Platek set theory).
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