Errata : «Facteurs et plans. I : Structure de finesse»
Extension of Boolean homomorphisms with bounding semimorphisms.
Extensions dans les treillis
Extensions of mappings of finite Boolean algebras to homomorphisms
Facteurs et plans. I : Structure de finesse
Filters in partially ordered sets
Flocks in universal and Boolean algebras
We propose the notion of flocks, which formerly were introduced only in based algebras, for any universal algebra. This generalization keeps the main properties we know from vector spaces, e.g. a closure system that extends the subalgebra one. It comes from the idempotent elementary functions, we call "interpolators", that in case of vector spaces merely are linear functions with normalized coefficients. The main example, we consider outside vector spaces, concerns Boolean algebras,...
Forcing for hL and hd
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.
Free products and elementary types of Boolean Algebras.
Free Suslin algebras
Full embeddings into the categories of Boolean algebras
Game properties of Boolean algebras
Generalizations of Boolean algebras. An attribute exploration
Generalized free products
A subalgebra B of the direct product of Boolean algebras is finitely closed if it contains along with any element f any other member of the product differing at most at finitely many places from f. Given such a B, let B* be the set of all members of B which are nonzero at each coordinate. The generalized free product corresponding to B is the subalgebra of the regular open algebra with the poset topology on B* generated by the natural basic open sets. Properties of this product are developed....
Generating subsets of distributive lattices.
Gruppoide und boolesche Strukturen
Historic forcing for Depth
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.
Homeomorphisms of products of Boolean separable spaces
Horizontal sums of basic algebras
The variety of basic algebras is closed under formation of horizontal sums. We characterize when a given basic algebra is a horizontal sum of chains, MV-algebras or Boolean algebras.
Ideal independence, free sequences, and the ultrafilter number
We make use of a forcing technique for extending Boolean algebras. The same type of forcing was employed in Baumgartner J.E., Komjáth P., Boolean algebras in which every chain and antichain is countable, Fund. Math. 111 (1981), 125–133, Koszmider P., Forcing minimal extensions of Boolean algebras, Trans. Amer. Math. Soc. 351 (1999), no. 8, 3073–3117, and elsewhere. Using and modifying a lemma of Koszmider, and using CH, we obtain an atomless BA, such that , answering questions raised by Monk...