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On Weak Theories of Sets and Classes which are Based on Strict ∏11-REFLECTION

Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (21-23):321-332 (1985)

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A proof-theoretic characterization of the primitive recursive set functions.Michael Rathjen - 1992 - Journal of Symbolic Logic 57 (3):954-969.details Let KP- be the theory resulting from Kripke-Platek set theory by restricting Foundation to Set Foundation. Let G: V → V (V:= universe of sets) be a ▵0-definable set function, i.e. there is a ▵0-formula φ(x, y) such that φ(x, G(x)) is true for all sets x, and $V \models \forall x \exists!y\varphi (x, y)$ . In this paper we shall verify (by elementary proof-theoretic methods) that the collection of set functions primitive recursive in G coincides with the collection of (...) Download Export citation Bookmark 11 citations
An ordinal analysis of admissible set theory using recursion on ordinal notations.Jeremy Avigad - 2002 - Journal of Mathematical Logic 2 (1):91-112.details The notion of a function from ℕ to ℕ defined by recursion on ordinal notations is fundamental in proof theory. Here this notion is generalized to functions on the universe of sets, using notations for well orderings longer than the class of ordinals. The generalization is used to bound the rate of growth of any function on the universe of sets that is Σ1-definable in Kripke–Platek admissible set theory with an axiom of infinity. Formalizing the argument provides an ordinal analysis. Download Export citation Bookmark 1 citation

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