Successor levels of the Jensen hierarchy

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


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



    Upload a copy of this work     Papers currently archived: 91,322

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

P-hierarchy on β ω.Andrzej Starosolski - 2008 - Journal of Symbolic Logic 73 (4):1202-1214.
Supercomplete extenders and type 1 mice: Part I.Q. Feng & R. Jensen - 2004 - Annals of Pure and Applied Logic 128 (1-3):1-73.
Rudimentary Languages and Second‐Order Logic.Malika More & Frédéric Olive - 1997 - Mathematical Logic Quarterly 43 (3):419-426.
A hierarchy of hereditarily finite sets.Laurence Kirby - 2008 - Archive for Mathematical Logic 47 (2):143-157.
Δ1 Ultrapowers are totally rigid.T. G. McLaughlin - 2007 - Archive for Mathematical Logic 46 (5-6):379-384.
Ultrapowers without the axiom of choice.Mitchell Spector - 1988 - Journal of Symbolic Logic 53 (4):1208-1219.
Development (and Evolution) of the Universe.Stanley N. Salthe - 2010 - Foundations of Science 15 (4):357-367.
On Some Autonomy Arguments in Social Science.Thomas Nickles - 1976 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1976:12-24.
Square in core models.Ernest Schimmerling & Martin Zeman - 2001 - Bulletin of Symbolic Logic 7 (3):305-314.


Added to PP

19 (#771,453)

6 months
2 (#1,244,653)

Historical graph of downloads
How can I increase my downloads?

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.

Add more citations

References found in this work

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

Add more references