The Ramified Analytical Hierarchy Using Extended Logics

Research output: Contribution to journalArticle (Academic Journal)peer-review

249 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)306-318
Number of pages13
JournalBulletin of Symbolic Logic
Issue number3
Publication statusPublished - Sep 2018

Bibliographical note

Published online: 25 October 2018


  • definability
  • analytical hierarchy
  • determinacy


Dive into the research topics of 'The Ramified Analytical Hierarchy Using Extended Logics'. Together they form a unique fingerprint.

Cite this