Embedding of Boolean algebras in Ρ(ω)/fin

J. Baumgartner; R. Frankiewicz; P. Zbierski

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On a theorem of Baumgartner and Weese

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A rigid Boolean algebra that admits the elimination of Q21

H. Mildenberg (1993)

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Using ♢ , we construct a rigid atomless Boolean algebra that has no uncountable antichain and that admits the elimination of the Malitz quantifier $Q_{1}^{2}$ .

On Monk’s questions

Saharon Shelah (1996)

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We deal with Boolean algebras and their cardinal functions: π-weight π and π-character πχ. We investigate the spectrum of π-weights of subalgebras of a Boolean algebra B. Next we show that the π-character of an ultraproduct of Boolean algebras may be different from the ultraproduct of the π-characters of the factors.

Openly generated Boolean algebras and the Fodor-type reflection principle

Sakaé Fuchino, Assaf Rinot (2011)

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We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is ℵ₂-projective. Previously it was known that this characterization of openly generated Boolean algebras follows from Axiom R. Since FRP is preserved by c.c.c. generic extension, we conclude in particular that this characterization is consistent with any set-theoretic assertion forcable by a c.c.c. poset starting from a model of FRP. A...