Atomic saturation of reduced powers

Our aim was to try to generalize some theorems about the saturation of ultrapowers to reduced powers. Naturally, we deal with saturation for types consisting of atomic formulas. We succeed to generalize “the theory of dense linear order (or T with the strict order property) is maximal and so is any...

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Bibliographic Details
Published in:Mathematical logic quarterly 2021-02, Vol.67 (1), p.18-42
Main Author: Shelah, Saharon
Format: Article
Language:English
Subjects:
Saturation
Theorems
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Summary:Our aim was to try to generalize some theorems about the saturation of ultrapowers to reduced powers. Naturally, we deal with saturation for types consisting of atomic formulas. We succeed to generalize “the theory of dense linear order (or T with the strict order property) is maximal and so is any pair(T,Δ) which is SOP3”, (where Δ consists of atomic or conjunction of atomic formulas). However, the theorem on “it is enough to deal with symmetric pre‐cuts” (so the p=t theorem) cannot be generalized in this case. Similarly the uniqueness of the dual cofinality fails in this context.
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.201900006