Introduction to Forcing

  • Gaisi Takeuti
  • Wilson M. Zaring
Part of the Graduate Texts in Mathematics book series (GTM, volume 1)

Abstract

In proving that AC and GCH are consistent with ZF, Gödel used the so called method of internal models. From the assumption that the universe V is a model of ZF Gödel prescribed a method for producing a submodel L that is also a model of V = L, AC and GCH. This submodel is defined as the class of all sets having a certain property, i.e.,
$$ L = \left\{ {x\left| {\left( {\exists \alpha } \right)\left[ {x = F'\alpha } \right]} \right|} \right\} $$
.

Keywords

Assure 

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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • Gaisi Takeuti
    • 1
  • Wilson M. Zaring
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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