Atomic saturation of reduced powers

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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 (Formula presented.) 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 (Formula presented.) theorem) cannot be generalized in this case. Similarly the uniqueness of the dual cofinality fails in this context.

Original languageEnglish
Pages (from-to)18-42
Number of pages25
JournalMathematical Logic Quarterly
Volume67
Issue number1
DOIs
StatePublished - Feb 2021

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