recursively inaccessible and Mahlo - Semantic Scholar
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recursively inaccessible and Mahlo - Semantic Scholar
Gerhard Jäger, Institut für Informatik und angewandte Mathematik, Universität. Bern, Neubrückstrasse 10, CH-3012 Bern, Switzerland, jaeger@iam.unibe.ch. 21.
First order theories for nonmonotone inductive definitions: recursively inaccessible and Mahlo Gerhard J¨ager Abstract In this paper first order theories for nonmonotone inductive definitions are introduced, and a proof-theoretic analysis for such theories based on combined operator forms `a la Richter with recursively inaccessible and Mahlo closure ordinals is given.
1
Introduction
Let Φ be an operator on the power set P (N) of the natural numbers, i.e. a mapping from P (N) to P (N). Then Φ can be used to generate subsets IΦσ of the natural numbers if we define [ and IΦ