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Ultraproducts

  • Kenneth A. Bowen
Chapter
  • 113 Downloads
Part of the Synthese Library book series (SYLI, volume 127)

Abstract

As in classical model theory, the construction of ultraproducts will be a very important tool in our development of modal model theory. Given an arbitrary non-empty index set I and a sequence <𝕬 i :iI> of modal structures for the language ML, we define the cartesian product X i∈I 𝕬i to be the following modal structure <B l,L,S,P,M> for ML. For each i, let 𝕬i = <A k i , Ki, Ri, Oi, Ni>. Then set L = X i∈I Ki the ordinary set-theoretic cartesian product, and for l,ĺL, define l Slĺ iff ∀i∈I[l(i)R iĺ(i)].

Keywords

Modal Structure Regular Cardinal Canonical Embedding Existential Closure Elementary Embedding 
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 Science+Business Media Dordrecht 1979

Authors and Affiliations

  • Kenneth A. Bowen
    • 1
  1. 1.Syracuse UniversityUSA

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