Abstract
IfT is a complete theory of Boolean algebra, then we writeA ⊲TB to denote that for every cardinal κ and every κ-regular filter over a setI such that the Boolean algebra 2FI of all subsets ofI reduced byF is a model ofT, the reduced powerAFI isK+-saturated wheneverBFI 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 ⊲TB andB ⊲TA. 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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