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The Ramified Analytical Hierarchy Using Extended Logics

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)306-318
Number of pages13
JournalBulletin of Symbolic Logic
Issue number3
DateAccepted/In press - 24 Aug 2018
DatePublished (current) - Sep 2018


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.

Additional information

Published online: 25 October 2018

    Research areas

  • definability, analytical hierarchy, determinacy

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    Accepted author manuscript, 276 KB, PDF document


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