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THE RAMIFIED ANALYTICAL HIERARCHY USING EXTENDED LOGICS

Published online by Cambridge University Press:  25 October 2018

PHILIP D. WELCH
PHILIP D. WELCH*
Affiliation:
SCHOOL OF MATHEMATICS UNIVERSITY OF BRISTOL BRISTOL, BS8 1TW, UKE-mail: p.welch@bristol.ac.uk
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Abstract

The use of Extended Logics to replace ordinary second order definability in Kleene’s Ramified Analytical Hierarchy is investigated. This mirrors a similar investigation of Kennedy, Magidor and Väänänen [11] where Gödel’s universe L of constructible sets is subjected to similar variance. Enhancing second order definability allows models to be defined which may or may not coincide with the original Kleene hierarchy in domain. Extending the logic with game quantifiers, and assuming strong axioms of infinity, we obtain minimal correct models of analysis. A wide spectrum of models can be so generated from abstract definability notions: one may take an abstract Spector Class and extract an extended logic for it. The resultant structure is then a minimal model of the given kind of definability.

Keywords

03E6003E1503E47definabilityanalytical hierarchydeterminacy
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 24 , Issue 3 , September 2018 , pp. 306 - 318
Copyright
Copyright © The Association for Symbolic Logic 2018 

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