Remarks on measurable Boolean algebras and sequential cardinals

Sequential Continuity and Submeasurable Cardinals

Submeasurable cardinals are deened in a similar way as measurable cardinals are. Their characterizations are given by means of sequentially continuous pseudonorms (or homomorphisms) on topological groups and of sequentially continuous (or uniformly continuous) functions on Cantor spaces (for that purpose it is proved that if a complete Boolean algebra admits a nonconstant sequentially continuou...

σ-Entangled Linear Orders and Narrowness of Products of Boolean Algebras

We investigate σ-entangled linear orders and narrowness of Boolean algebras. We show existence of σ-entangled linear orders in many cardinals, and we build Boolean algebras with neither large chains nor large pies. We study the behavior of these notions in ultraproducts. ∗ Partially supported by the Deutsche Forschungsgemeinschaft, Grant No. Ko 490/7-1. Publication 462.

Complete Quotient Boolean Algebras

For I a proper, countably complete ideal on P(X) for some set X , can the quotient Boolean algebra P(X)/I be complete? This question was raised by Sikorski [Si] in 1949. By a simple projection argument as for measurable cardinals, it can be assumed that X is an uncountable cardinal κ, and that I is a κ-complete ideal on P(κ) containing all singletons. In this paper we provide consequences from ...

Complete Embeddings of the Cohen Algebra into Three Families of C.c.c., Non-measurable Boolean Algebras

Von Neumann conjectured that the countable chain condition and the weak (ω, ω)-distributive law characterize measurable algebras among Boolean σalgebras [Mau]. Consistent counter-examples have been obtained by Maharam [Mah], Jensen [J], Glówczyński [Gl], and Veličković [V]. However, whether von Neumann’s proposed characterization of measurable algebras fails within ZFC remains an open problem. ...

Continuum Cardinals Generalized to Boolean Algebras