On spaces in which a bound on certain cardinal invariants implies closedness
D. L. Grant, I. L. Reilly (1990)
Matematički Vesnik
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D. L. Grant, I. L. Reilly (1990)
Matematički Vesnik
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Samuel Coskey, Tamás Mátrai, Juris Steprāns (2013)
Fundamenta Mathematicae
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We discuss the Borel Tukey ordering on cardinal invariants of the continuum. We observe that this ordering makes sense for a larger class of cardinals than has previously been considered. We then provide a Borel version of a large portion of van Douwen's diagram. For instance, although the usual proof of the inequality 𝔭 ≤ 𝔟 does not provide a Borel Tukey map, we show that in fact there is one. Afterwards, we revisit a result of Mildenberger concerning a generalization of the unsplitting...
Joanna Jureczko (2017)
Open Mathematics
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In this paper we will show some relations between generalized versions of strong sequences introduced by Efimov in 1965 and independent families. We also show some inequalities between cardinal invariants associated with these both notions.
G. P. Monro (1974)
Colloquium Mathematicae
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Arthur W. Apter (2013)
Bulletin of the Polish Academy of Sciences. Mathematics
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We investigate two global GCH patterns which are consistent with the existence of a tall cardinal, and also present some related open questions.
Arthur W. Apter (2012)
Fundamenta Mathematicae
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We apply techniques due to Sargsyan to reduce the consistency strength of the assumptions used to establish an indestructibility theorem for supercompactness. We then show how these and additional techniques due to Sargsyan may be employed to establish an equiconsistency for a related indestructibility theorem for strongness.
Arthur W. Apter, Grigor Sargsyan (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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We show how to reduce the assumptions in consistency strength used to prove several theorems on universal indestructibility.
A. Wojciechowska (1972)
Fundamenta Mathematicae
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Josef Šlapal (1993)
Czechoslovak Mathematical Journal
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Andreas Blass, Ioanna M. Dimitriou, Benedikt Löwe (2007)
Fundamenta Mathematicae
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We consider four notions of strong inaccessibility that are equivalent in ZFC and show that they are not equivalent in ZF.
Arthur W. Apter (2015)
Bulletin of the Polish Academy of Sciences. Mathematics
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We construct a model for the level by level equivalence between strong compactness and supercompactness with an arbitrary large cardinal structure in which the least supercompact cardinal κ has its strong compactness indestructible under κ-directed closed forcing. This is in analogy to and generalizes the author's result in Arch. Math. Logic 46 (2007), but without the restriction that no cardinal is supercompact up to an inaccessible cardinal.
Sy-David Friedman (2009)
Acta Universitatis Carolinae. Mathematica et Physica
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E. Kleinberg (1979)
Fundamenta Mathematicae
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Arthur W. Apter (2012)
Bulletin of the Polish Academy of Sciences. Mathematics
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We show that certain relatively consistent structural properties of the class of supercompact cardinals are also relatively consistent with the Wholeness Axioms.
Angelo Bella, Peter Nyikos (2010)
Colloquium Mathematicae
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The general question of when a countably compact topological space is sequentially compact, or has a nontrivial convergent sequence, is studied from the viewpoint of basic cardinal invariants and small uncountable cardinals. It is shown that the small uncountable cardinal 𝔥 is both the least cardinality and the least net weight of a countably compact space that is not sequentially compact, and that it is also the least hereditary Lindelöf degree in most published models. Similar results,...