On BPI Restricted to Boolean Algebras of Size Continuum

• Autorzy: Eric Hall , Kyriakos Keremedis
• Języki publikacji: EN

Abstrakty

EN

(i) The statement P(ω) = "every partition of ℝ has size ≤ |ℝ|" is equivalent to the proposition R(ω) = "for every subspace Y of the Tychonoff product $2^{𝓟(ω)}$ the restriction 𝓑|Y = {Y ∩ B: B ∈ 𝓑} of the standard clopen base 𝓑 of $2^{𝓟(ω)}$ to Y has size ≤ |𝓟(ω)|".
(ii) In ZF, P(ω) does not imply "every partition of 𝓟(ω) has a choice set".
(iii) Under P(ω) the following two statements are equivalent:
(a) For every Boolean algebra of size ≤ |ℝ| every filter can be extended to an ultrafilter.
(b) Every Boolean algebra of size ≤ |ℝ| has an ultrafilter.

Kategorie tematyczne

• 06E25: Boolean algebras with additional operations (diagonalizable algebras, etc.)
• 03E25: Axiom of choice and related propositions
• 03G05: Boolean algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2013
• Tom: 61
• Numer: 1
• Strony: 9-21

Daty

wydano

2013

Twórcy

autor

Eric Hall

• Department of Mathematics & Statistics, College of Arts & Sciences, University of Missouri - Kansas City, 206 Haag Hall, 5100 Rockhill Rd, Kansas City, MO 64110, USA

autor

Kyriakos Keremedis

• Department of Mathematics, University of the Aegean, Karlovassi, Samos 83200, Greece

Identyfikatory

DOI

10.4064/ba61-1-2