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Cohen’s Method

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

Abstract

In proving that the AC and the 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.
$${{L}^{\mathcal{M}}} = \left\{ {a\left| {\left( {\exists \alpha \in \mathcal{M}} \right)\left[ {a = F{}^\backprime \alpha } \right]} \right.} \right\}$$
.

Keywords

Minimal Model Internal Model Free Variable Axiom Schema Fundamental Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1971

Authors and Affiliations

  • Gaisi Takeuti
    • 1
  • Wilson M. Zaring
    • 1
  1. 1.University of IllinoisUSA

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