Rosenthal families, pavings and generic cardinal invariants

Proceedings of the American Mathematical Society ◽

10.1090/proc/15252 ◽

2020 ◽

pp. 1

Author(s):

Piotr Koszmider ◽

Arturo Martínez-Celis

Keyword(s):

Cardinal Invariants

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Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle

Bulletin of Symbolic Logic ◽

10.2178/bsl/1130335207 ◽

2005 ◽

Vol 11 (4) ◽

pp. 517-525

Author(s):

Juris Steprāns

Keyword(s):

Harmonic Analysis ◽

Set Theory ◽

Harmonic Functions ◽

Maximal Functions ◽

Pigeonhole Principle ◽

Cardinal Invariants ◽

Geometric Objects

AbstractIt is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.

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CARDINAL INVARIANTS AND SETS OF REALS

Real Analysis Exchange ◽

10.2307/44153886 ◽

1995 ◽

Vol 21 (1) ◽

pp. 78

Author(s):

Bartoszyński

Keyword(s):

Cardinal Invariants

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Converse dual cardinals

Journal of Symbolic Logic ◽

10.2178/jsl/1140641161 ◽

2006 ◽

Vol 71 (1) ◽

pp. 22-34 ◽

Cited By ~ 4

Author(s):

Jörg Brendle ◽

Shuguo Zhang

Keyword(s):

Natural Numbers ◽

Cardinal Invariants ◽

The Continuum

AbstractWe investigate the set (ω) of partitions of the natural numbers ordered by ≤* where A ≤* B if by gluing finitely many blocks of A we can get a partition coarser than B. In particular, we determine the values of a number of cardinals which are naturally associated with the structure ((ω), ≥*), in terms of classical cardinal invariants of the continuum.

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