Archive for Mathematical Logic

, Volume 39, Issue 4, pp 227–251 | Cite as

Generic relativizations of fine structure

  • Kai Hauser


It is shown how certain generic extensions of a fine structural model in the sense of Mitchell and Steel [MiSt] can be reorganized as relativizations of the model to the generic object. This is then applied to the construction of Steel's core model for one Woodin cardinal [St] and its generalizations.

Mathematics Subject Classification (2000): Primary 03E45, 03E40. Secondary 03E55, 03E35, 03E60. 
Key words and phrases: set theory/fine structure/forcing/generic extensions/core models. 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Kai Hauser
    • 1
  1. 1.Department of Mathematics, University of California, Berkeley, CA 94720, USA (
  2. 2.Lehrstuhl für Mathematische Logik, Humboldt Universität zu Berlin, D-10099 Berlin, Germany (

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