Successor levels of the Jensen hierarchy

Mathematical Logic Quarterly 55 (1):4-20 (2009)
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Abstract

I prove that there is a recursive function T that does the following: Let X be transitive and rudimentarily closed, and let X ′ be the closure of X ∪ {X } under rudimentary functions. Given a Σ0-formula φ and a code c for a rudimentary function f, T is a Σω-formula such that for any equation image ∈ X, X ′ ⊧ φ [f ] iff X ⊧ T [equation image]. I make this precise and show relativized versions of this. As an application, I prove that under certain conditions, if Y is the Σω extender ultrapower of X with respect to some extender F that also is an extender on X ′, then the closure of Y ∪ {Y } under rudimentary functions is the Σ0 extender ultrapower of X′ with respect to F, and the ultrapower embeddings agree on X

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Citations of this work

λ-structures and s-structures: Translating the models.Gunter Fuchs - 2011 - Annals of Pure and Applied Logic 162 (4):257-317.
λ-structures and s-structures: Translating the iteration strategies.Gunter Fuchs - 2011 - Annals of Pure and Applied Logic 162 (9):710-751.

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References found in this work

The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.

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