منابع مشابه
Constructing Boolean Algebras for Cardinal Invariants
We construct Boolean Algebras answering some questions of J. Donald Monk on cardinal invariants. The results are proved in ZFC (rather than giving consistency results). We deal with the existence of superatomic Boolean Algebras with “few automorphisms”, with entangled sequences of linear orders, and with semi-ZFC examples of the non-attainment of the spread (and hL,hd).
متن کاملCardinal invariants of ultraproducts of Boolean algebras
We deal with some of problems posed by Monk [Mo 1], [Mo 3] and related to cardinal invariant of ultraproducts of Boolean algebras. We also introduce and investigate several new cardinal invariants. AMS 1991 Mathematics Subject Classification primary: 03G05, 03E05, secondary: 06E15, 03E35 ∗ The research was partially supported by DFG grant Ko 490/7-1. This is publication number 534 of the second...
متن کاملMore on Cardinal Invariants of Boolean Algebras
We address several questions of Donald Monk related to irredundance and spread of Boolean algebras, gaining both some ZFC knowledge and consistency results. We show in ZFC that irr(B0 × B1) = max{irr(B0), irr(B1)}. We prove consistency of the statement “there is a Boolean algebra B such that irr(B) < s(B ~ B)” and we force a superatomic Boolean algebra B∗ such that s(B∗) = inc(B∗) = κ, irr(B∗) ...
متن کاملOn Cardinal Invariants and Generators for Von Neumann Algebras
We demonstrate how virtually all common cardinal invariants associated to a von Neumann algebra M can be computed from the decomposability number, dec(M), and the minimal cardinality of a generating set, gen(M). Applications include the equivalence of the well-known generator problem, “Is every separably-acting von Neumann algebra singly-generated?”, with the formally stronger questions, “Is ev...
متن کاملOn incomparability and related cardinal functions on ultraproducts of Boolean algebras
Let C denote any of the following cardinal characteristics of Boolean algebras: incomparability, spread, character, π-character, hereditary Lindelöf number, hereditary density. It is shown to be consistent that there exists a sequence 〈Bi : i < κ〉 of Boolean algebras and an ultrafilter D on κ such that
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2021
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm922-6-2020