-theories of Boolean algebras
A characterization of complete atomic Boolean algebra.
In this note we give a characterization of complete atomic Boolean algebras by means of complete atomic lattices. We find that unicity of the representation of the maximum as union of atoms and Lambda-infinite distributivity law are necessary and sufficient conditions for the lattice to be a complete atomic Boolean algebra.
A Complete Boolean Algebra without Homogeneous or Rigid Factors.
A forcing construction of thin-tall Boolean algebras
It was proved by Juhász and Weiss that for every ordinal α with there is a superatomic Boolean algebra of height α and width ω. We prove that if κ is an infinite cardinal such that and α is an ordinal such that , then there is a cardinal-preserving partial order that forces the existence of a superatomic Boolean algebra of height α and width κ. Furthermore, iterating this forcing through all , we obtain a notion of forcing that preserves cardinals and such that in the corresponding generic...
A Functional Approach to the Theory of Prime Implicants
A Galois correspondence for boolean algebras
A groupoid characterization of Boolean algebras
We present a groupoid which can be converted into a Boolean algebra with respect to term operations. Also conversely, every Boolean algebra can be reached in this way.
A note on Boolean algebras
We show that splitting of elements of an independent family of infinite regular size will produce a full size independent set.
A Note On Reproductive Solutions
A note on reproductive solutions.
A problem of Halmos on projective Boolean algebras
A Remark on Subsets of Free Boolean Algebras
A selection theorem for Boolean correspondences.
A set-theoretical equivalent of the prime ideal theorem for Boolean algebras
Algebraic characterizations of special Boolean rings
An extension of the Stone representation for orthomodular lattices
Another note on countable Boolean algebras
We prove that a Boolean algebra is countable iff its subalgebra lattice admits a continuous complementation.
Any orthomodular poset is a pasting of Boolean algebras
Atomicity of the Boolean algebra of direct factors of a directed set
In the present paper we deal with the relations between direct product decompositions of a directed set and direct product decompositions of intervals of .
Atoms and Generators in Boolean -Algebras