Displaying similar documents to “Historic forcing for Depth”

On Monk’s questions

Saharon Shelah (1996)

Fundamenta Mathematicae

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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.

Forcing for hL and hd

Andrzej Rosłanowski, Saharon Shelah (2001)

Colloquium Mathematicae

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The present paper addresses the problem of attainment of the supremums in various equivalent definitions of the hereditary density hd and hereditary Lindelöf degree hL of Boolean algebras. We partially answer two problems of J. Donald Monk [13, Problems 50, 54], showing consistency of different attainment behaviour and proving that (for the variants considered) this is the best result we can expect.

The elementary-equivalence classes of clopen algebras of P-spaces

Brian Wynne (2008)

Fundamenta Mathematicae

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Two Boolean algebras are elementarily equivalent if and only if they satisfy the same first-order statements in the language of Boolean algebras. We prove that every Boolean algebra is elementarily equivalent to the algebra of clopen subsets of a normal P-space.

Openly generated Boolean algebras and the Fodor-type reflection principle

Sakaé Fuchino, Assaf Rinot (2011)

Fundamenta Mathematicae

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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...

A note on Boolean algebras

Isaac Gorelic (1994)

Commentationes Mathematicae Universitatis Carolinae

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We show that splitting of elements of an independent family of infinite regular size will produce a full size independent set.