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On models with power-like orderings

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah
Affiliation:
Hebrew University, Jerusalem, Israel Princeton University, Princeton, New Jersey 08540

Abstract

We prove here theorems of the form: if T has a model M in which P1(M) is κ1-like ordered, P2(M) is κ2-like ordered …, and Q1(M) is of power λ1, …, then T has a model N in which P1(M) is κ1-like ordered …, Q1(N) is of power λ1, …. (In this article κ is a strong-limit singular cardinal, and κ′ is a singular cardinal.)

We also sometimes add the condition that M, N omits some types. The results are seemingly the best possible, i.e. according to our knowledge about n-cardinal problems (or, more precisely, a certain variant of them).

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1972

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