Ultrafilter translations |
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Authors: | Paolo Lipparini |
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Institution: | (1) Dipartimento di Mathematica, Universitá di Roma (Tor Vergata), I-00133 Rome, Italy |
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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 > then the logic with the quantifier there exist many is (,)-compact if and only if either is weakly compact or is singular of cofinality<. As a corollary, for every infinite cardinals and , there exists a (,)-compact non-(,)-compact logic if and only if either < orcf<cf or < is weakly compact.Counterexamples are given showing that the above statements may fail, ifV=L is not assumed.However, without special assumptions, analogous results are obtained for the stronger notion of ,]-compactness. |
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Keywords: | primary 03C20 03C80 03C95 secondary 03E55 03E45 03C75 |
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