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Reduced products which are not saturated

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Summary

IfT is a complete theory of Boolean algebra, then we writeA ⊲T B to denote that for every cardinal κ and every κ-regular filter over a setI such that the Boolean algebra 2 F I of all subsets ofI reduced byF is a model ofT, the reduced powerA F I isK +-saturated wheneverB F I isK +-saturated. The relation ⊲T generalizes the relation ◃ introduced by Keisler. As in the case of Keisler's ◃ it happens that ⊲T’s are relations between complete theories, i.e. ifA≡B thenA ⊲T B andB ⊲T A. In this paper some examples of theories which are maximal (minimal) with respect to ⊲T’s are provided and the relations ⊲T are compared with each other.

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Authors and Affiliations

  1. Polish Academy of Sciences, Wroław, Poland

    Leszek Pacholski & Jerzy Tomasik

  2. University of Wrocław, Wrocław, Poland

    Leszek Pacholski & Jerzy Tomasik

Authors
  1. Leszek Pacholski
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  2. Jerzy Tomasik
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Pacholski, L., Tomasik, J. Reduced products which are not saturated. Algebra Universalis 14, 210–227 (1982). https://doi.org/10.1007/BF02483921

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  • DOI: https://doi.org/10.1007/BF02483921

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AMS (MOS) classification 02H13

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