Ultrafilter translations

Archive for Mathematical Logic 35 (2):63-87 (1996)
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Abstract

We develop a method for extending results about ultrafilters into a more general setting. In this paper we shall be mainly concerned with applications to cardinality logics. For example, assumingV=L, Gödel's Axiom of Constructibility, we prove that if λ > ωα then the logic with the quantifier “there existα many” is (λ,λ)-compact if and only if either λ is weakly compact or λ is singular of cofinality<ωα. As a corollary, for every infinite cardinals λ and μ, there exists a (λ,λ)-compact non-(μ,μ)-compact logic if and only if either λ<μ orcfλ

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10.1007/bf01273686

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Citations of this work

More on regular and decomposable ultrafilters in ZFC.Paolo Lipparini - 2010 - Mathematical Logic Quarterly 56 (4):340-374.
Decomposable Ultrafilters and Possible Cofinalities.Paolo Lipparini - 2008 - Notre Dame Journal of Formal Logic 49 (3):307-312.

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References found in this work

Models and Ultraproducts: An Introduction.J. L. Bell & A. B. Slomson - 1972 - Journal of Symbolic Logic 37 (4):763-764.
The weak □* is really weaker than the full □.Shai Ben-David & Menachem Magidor - 1986 - Journal of Symbolic Logic 51 (4):1029 - 1033.
Limit ultrapowers and abstract logics.Paolo Lipparini - 1987 - Journal of Symbolic Logic 52 (2):437-454.
The Theory of Ultrafilters.W. W. Comfort & S. Negrepontis - 1976 - Journal of Symbolic Logic 41 (4):782-783.

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