Homogeneity, universality and saturatedness of limit reduced powers I
J. Wierzejewski (1977)
Fundamenta Mathematicae
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J. Wierzejewski (1977)
Fundamenta Mathematicae
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Jana Flašková (2005)
Acta Universitatis Carolinae. Mathematica et Physica
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Brian L. Davis, Iwo Labuda (2007)
Mathematica Slovaca
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Itay Neeman, Jindřich Zapletal (1998)
Commentationes Mathematicae Universitatis Carolinae
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We show that in the presence of large cardinals proper forcings do not change the theory of with real and ordinal parameters and do not code any set of ordinals into the reals unless that set has already been so coded in the ground model.
D. C. Kent (1968)
Fundamenta Mathematicae
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Zvonimir Šikić (2020)
Bulletin of the Section of Logic
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We prove a characterization theorem for filters, proper filters and ultrafilters which is a kind of converse of Łoś's theorem. It is more natural than the usual intuition of these terms as large sets of coordinates, which is actually unconvincing in the case of ultrafilters. As a bonus, we get a very simple proof of Łoś's theorem.