TY - JOUR
T1 - Atomic saturation of reduced powers
AU - Shelah, Saharon
N1 - Publisher Copyright:
© 2021 Wiley-VCH GmbH
PY - 2021/2
Y1 - 2021/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85106212221&partnerID=8YFLogxK
U2 - 10.1002/malq.201900006
DO - 10.1002/malq.201900006
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AN - SCOPUS:85106212221
SN - 0942-5616
VL - 67
SP - 18
EP - 42
JO - Mathematical Logic Quarterly
JF - Mathematical Logic Quarterly
IS - 1
ER -