On the extent of separable, locally compact, selectively (a)-spaces

• Autorzy: Samuel G. da Silva
• Języki publikacji: EN

Abstrakty

EN

The author has recently shown (2014) that separable, selectively (a)-spaces cannot include closed discrete subsets of size 𝔠. It follows that, assuming CH, separable selectively (a)-spaces necessarily have countable extent. However, in the same paper it is shown that the weaker hypothesis "$2^{ℵ₀} < 2^{ℵ₁}$" is not enough to ensure the countability of all closed discrete subsets of such spaces. In this paper we show that if one adds the hypothesis of local compactness, a specific effective (i.e., Borel) parametrized weak diamond principle implies countable extent in this context.

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 03E05: Other combinatorial set theory
• 03E65: Other hypotheses and axioms
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 54A35: Consistency and independence results
• 54D45: Local compactness, σ -compactness

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 141
• Numer: 2
• Strony: 199-208

Daty

wydano

2015

Twórcy

autor

Samuel G. da Silva

• Instituto de Matemática, Universidade Federal da Bahia, Av. Adhemar de Barros, S/N, Ondina, CEP 40170-110, Salvador, BA, Brazil

Identyfikatory

DOI

10.4064/cm141-2-5