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- W4289702197 abstract "The use of Extended Logics to replace ordinary second order definability in Kleene's {em Ramified Analytical Hierarchy} is investigated. This mirrors a similar investigation of Kennedy, Magidor and Vaananen cite{KeMaVa2016} where Godel'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 {em 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." @default.
- W4289702197 created "2022-08-04" @default.
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- W4289702197 date "2018-08-11" @default.
- W4289702197 modified "2023-09-29" @default.
- W4289702197 title "The Ramified Analytical Hierarchy using Extended Logics" @default.
- W4289702197 doi "https://doi.org/10.48550/arxiv.1808.03814" @default.
- W4289702197 hasPublicationYear "2018" @default.
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