A Boolean Algebra with Few Subalgebras, Interval Boolean Algebras and Retractiveness

DOI10.2307/1999302zbMath0524.06020OpenAlexW4230635840MaRDI QIDQ3037505

Matatyahu Rubin

Publication date: 1983

Full work available at URL: https://doi.org/10.2307/1999302

zbMATH Keywords

endomorphismsinterval algebranowhere dense setdiamond principlecountably generated idealretractive Boolean algebracountable densely ordered chaincountable independent setRotman's conjectureuncountable principal ideal

Mathematics Subject Classification ID

Consistency and independence results (03E35) Lattice ideals, congruence relations (06B10) Structure theory of Boolean algebras (06E05) Chain conditions, complete algebras (06E10)

Related Items (20)

Boolean Algebras with Few Endomorphisms ⋮ Vietoris hyperspaces over scattered Priestley spaces ⋮ Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations ⋮ Some questions about Boolean algebras ⋮ Large Irredundant Sets in Operator Algebras ⋮ More on cardinal invariants of Boolean algebras ⋮ Measures on minimally generated Boolean algebras ⋮ On subalgebras of Boolean interval algebras ⋮ Moderate families in Boolean algebras ⋮ Pseudo-trees and Boolean algebras ⋮ Quotients of Boolean algebras and regular subalgebras ⋮ A thin-tall Boolean algebra which is isomorphic to each of its uncountable subalgebras ⋮ Free Boolean algebras over unions of two well orderings ⋮ A note on irredundant sets ⋮ Independence in Boolean algebras ⋮ Narrow Boolean algebras ⋮ Complements and quasicomplements in the lattice of subalgebras of \(P(\omega)\) ⋮ Some properties of the lattice of subalgebras of a Boolean algebra ⋮ Uncountable constructions for B. A., e. c. groups and Banach spaces ⋮ Applications of Boolean powers of algebraic systems

Cites Work

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• Some questions about Boolean algebras
• Very strongly rigid Boolean algebras, continuum discrete set condition, countable antichain condition. I
• Boolean Algebras with Few Endomorphisms
• Simultaneous linear extension of Continuous functions
• Compact extensions of L(Q) (part 1a)
• Boolean algebras with ordered bases

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