A note on theories for quasi-inductive definitions

Review of Symbolic Logic 2 (4):684-699 (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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DOI 10.1017/S175502030909025X
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The Truth is Never Simple.John P. Burgess - 1986 - Journal of Symbolic Logic 51 (3):663-681.
Constructibility.Keith J. Devlin - 1987 - Journal of Symbolic Logic 52 (3):864-867.

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