Property ( a ) and dominating families

Samuel Gomes da Silva

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 4, page 667-684
  • ISSN: 0010-2628

Abstract

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Generalizations of earlier negative results on Property ( a ) are proved and two questions on an ( a ) -version of Jones’ Lemma are posed. We discuss these questions in the realm of locally compact spaces. Using dominating families of functions as a tool, we prove that under the assumptions “ 2 ω is regular” and “ 2 ω < 2 ω 1 ” the existence of a T 1 separable locally compact ( a ) -space with an uncountable closed discrete subset implies the existence of inner models with measurable cardinals. We also use cardinal invariants such as 𝔡 to prove results in the class of locally compact spaces that strengthen, in such class, the negative results mentioned above.

How to cite

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da Silva, Samuel Gomes. "Property $(a)$ and dominating families." Commentationes Mathematicae Universitatis Carolinae 46.4 (2005): 667-684. <http://eudml.org/doc/249527>.

@article{daSilva2005,
abstract = {Generalizations of earlier negative results on Property $(a)$ are proved and two questions on an $(a)$-version of Jones’ Lemma are posed. We discuss these questions in the realm of locally compact spaces. Using dominating families of functions as a tool, we prove that under the assumptions “$2^\omega $ is regular” and “$2^\omega < 2^\{\omega _1\}$” the existence of a $T_1$ separable locally compact $(a)$-space with an uncountable closed discrete subset implies the existence of inner models with measurable cardinals. We also use cardinal invariants such as $\mathfrak \{d\}$ to prove results in the class of locally compact spaces that strengthen, in such class, the negative results mentioned above.},
author = {da Silva, Samuel Gomes},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {property $(a)$; dominating families; small cardinals; inner models of measurability; small cardinals; inner models of measurability},
language = {eng},
number = {4},
pages = {667-684},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Property $(a)$ and dominating families},
url = {http://eudml.org/doc/249527},
volume = {46},
year = {2005},
}

TY - JOUR
AU - da Silva, Samuel Gomes
TI - Property $(a)$ and dominating families
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 4
SP - 667
EP - 684
AB - Generalizations of earlier negative results on Property $(a)$ are proved and two questions on an $(a)$-version of Jones’ Lemma are posed. We discuss these questions in the realm of locally compact spaces. Using dominating families of functions as a tool, we prove that under the assumptions “$2^\omega $ is regular” and “$2^\omega < 2^{\omega _1}$” the existence of a $T_1$ separable locally compact $(a)$-space with an uncountable closed discrete subset implies the existence of inner models with measurable cardinals. We also use cardinal invariants such as $\mathfrak {d}$ to prove results in the class of locally compact spaces that strengthen, in such class, the negative results mentioned above.
LA - eng
KW - property $(a)$; dominating families; small cardinals; inner models of measurability; small cardinals; inner models of measurability
UR - http://eudml.org/doc/249527
ER -

References

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  9. Szeptycki P.J., Vaughan J.E., Almost disjoint families and property ( a ) , Fund. Math. 158 3 (1998), 229-240. (1998) Zbl0933.54005MR1663330
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