Displaying similar documents to “Borel Tukey morphisms and combinatorial cardinal invariants of the continuum”

Around cofin

Andrzej Rosłanowski, Saharon Shelah (2014)

Colloquium Mathematicae

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We show the consistency of "there is a nice σ-ideal ℐ on the reals with add(ℐ) = ℵ₁ which cannot be represented as the union of a strictly increasing sequence of length ω₁ of σ-subideals". This answers [Borodulin-Nadzieja and Głąb, Math. Logic Quart. 57 (2011), 582-590, Problem 6.2(ii)].

Almost disjoint families and “never” cardinal invariants

Charles Morgan, Samuel Gomes da Silva (2009)

Commentationes Mathematicae Universitatis Carolinae

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We define two cardinal invariants of the continuum which arise naturally from combinatorially and topologically appealing properties of almost disjoint families of sets of the natural numbers. These are the never soft and never countably paracompact numbers. We show that these cardinals must both be equal to ω 1 under the effective weak diamond principle ♦ ( ω , ω , < ) , answering questions of da Silva S.G., On the presence of countable paracompactness, normality and property ( a ) in spaces from almost...

κ-strong sequences and the existence of generalized independent families

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.

A classification of ordinals up to Borel isomorphism

Su Gao, Steve Jackson, Vincent Kieftenbeld (2008)

Fundamenta Mathematicae

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We consider the Borel structures on ordinals generated by their order topologies and provide a complete classification of all ordinals up to Borel isomorphism in ZFC. We also consider the same classification problem in the context of AD and give a partial answer for ordinals ≤ω₂.

Separating equivalence classes

Jindřich Zapletal (2018)

Commentationes Mathematicae Universitatis Carolinae

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Given a countable Borel equivalence relation, I introduce an invariant measuring how difficult it is to find Borel sets separating its equivalence classes. I evaluate these invariants in several standard generic extensions.

Some applications of Sargsyan's equiconsistency method

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.

Some Remarks on Tall Cardinals and Failures of GCH

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.