Displaying similar documents to “Forcing for hL and hd”

Historic forcing for Depth

Andrzej Rosłanowski, Saharon Shelah (2001)

Colloquium Mathematicae

Similarity:

We show that, consistently, for some regular cardinals θ <λ, there exists a Boolean algebra 𝔹 such that |𝔹| = λ⁺ and for every subalgebra 𝔹'⊆ 𝔹 of size λ⁺ we have Depth(𝔹') = θ.

On Marczewski-Burstin representable algebras

Marek Balcerzak, Artur Bartoszewicz, Piotr Koszmider (2004)

Colloquium Mathematicae

Similarity:

We construct algebras of sets which are not MB-representable. The existence of such algebras was previously known under additional set-theoretic assumptions. On the other hand, we prove that every Boolean algebra is isomorphic to an MB-representable algebra of sets.

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

Brian Wynne (2008)

Fundamenta Mathematicae

Similarity:

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

Similarity:

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...

Two constructions of De Morgan algebras and De Morgan quasirings

Ivan Chajda, Günther Eigenthaler (2009)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

De Morgan quasirings are connected to De Morgan algebras in the same way as Boolean rings are connected to Boolean algebras. The aim of the paper is to establish a common axiom system for both De Morgan quasirings and De Morgan algebras and to show how an interval of a De Morgan algebra (or De Morgan quasiring) can be viewed as a De Morgan algebra (or De Morgan quasiring, respectively).

On Monk’s questions

Saharon Shelah (1996)

Fundamenta Mathematicae

Similarity:

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.

A common approach to directoids with an antitone involution and D-quasirings

Ivan Chajda, Miroslav Kolařík (2008)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

We introduce the so-called DN-algebra whose axiomatic system is a common axiomatization of directoids with an antitone involution and the so-called D-quasiring. It generalizes the concept of Newman algebras (introduced by H. Dobbertin) for a common axiomatization of Boolean algebras and Boolean rings.