Fragments of Kripke{platek Set Theory with Innnity
نویسنده
چکیده
In this paper we shall investigate fragments of Kripke{Platek set theory with Innnity which arise from the full theory by restricting Foundation to n Foundation, where n 2. The strength of such fragments will be characterized in terms of the smallest ordinal such that L is a model of every 2 sentence which is provable in the theory.
منابع مشابه
Relativized ordinal analysis: The case of Power Kripke-Platek set theory
The paper relativizes the method of ordinal analysis developed for KripkePlatek set theory to theories which have the power set axiom. We show that it is possible to use this technique to extract information about Power Kripke-Platek set theory, KP(P). As an application it is shown that whenever KP(P) + AC proves a Π2 statement then it holds true in the segment Vτ of the von Neumann hierarchy, ...
متن کاملAbout the strength of operational regularity
We analyze the consistency strength of regularity on the basis of Feferman’s operational set theory OST. Our main result shows that regularity over OST for operations corresponds to regularity with respect to set-theoretic functions in frameworks like Kripke-Platek set theory. As a consequence, we obtain that OST plus the operational axiom (Inac) is consistency-equivalent to Kripke-Platek set t...
متن کاملOperational closure and stability
In this article we introduce and study the notion of operational closure: a transitive set d is called operationally closed iff it contains all constants of OST and any operation f ∈ d applied to an element a ∈ d yields an element fa ∈ d, provided that f applied to a has a value at all. We will show that there is a direct relationship between operational closure and stability in the sense that ...
متن کاملUniverses in Type Theory Part II – Autonomous Mahlo
We introduce the autonomous Mahlo universe which is an extension of Martin-Löf type theory which we consider as predicatively justified and which has a strength which goes substantially beyond that of the Mahlo universe, which is before writing this paper the strongest predicatively justified published extension of Martin-Löf type theory. We conjecture it to have the same proof theoretic streng...
متن کاملUniverses in Type Theory Part I – Inaccessibles and Mahlo
We give an overview over universes in Martin-Löf type theory and consider the following universe constructions: a simple universe, E. Palmgren’s super universe and the Mahlo universe. We then introduce models for these theories in extensions of Kripke-Platek set theory having the same proof theoretic strength. The extensions of Kripke-Platek set theory used formalise the existence of a recursiv...
متن کامل