On models with power-like ordering

Journal of Symbolic Logic 37 (2):247-267 (1972)
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Abstract

We prove here theorems of the form: if T has a model M in which P 1 (M) is κ 1 -like ordered, P 2 (M) is κ 2 -like ordered ..., and Q 1 (M) if of power λ 1 , ..., then T has a model N in which P 1 (M) is κ 1 '-like ordered ..., Q 1 (N) is of power λ 1 ,.... (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)

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References found in this work

On models with large automorphism groups.H. -D. Ebbinghaus - 1971 - Archive for Mathematical Logic 14 (3-4):179-197.

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