-theories of Boolean algebras
A basis of the conjunctively polynomial-like Boolean functions.
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 characterization of polarities whose lattice of polars is Boolean
A C(K) Banach space which does not have the Schroeder-Bernstein property
We construct a totally disconnected compact Hausdorff space K₊ which has clopen subsets K₊” ⊆ K₊’ ⊆ K₊ such that K₊” is homeomorphic to K₊ and hence C(K₊”) is isometric as a Banach space to C(K₊) but C(K₊’) is not isomorphic to C(K₊). This gives two nonisomorphic Banach spaces (necessarily nonseparable) of the form C(K) which are isomorphic to complemented subspaces of each other (even in the above strong isometric sense), providing a solution to the Schroeder-Bernstein problem for Banach spaces...
A common abstraction of boolean rings and lattice ordered groups
A common approach to directoids with an antitone involution and D-quasirings
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.
A Complete Boolean Algebra without Homogeneous or Rigid Factors.
A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube
We compare the forcing-related properties of a complete Boolean algebra with the properties of the convergences (the algebraic convergence) and on generalizing the convergence on the Cantor and Aleksandrov cube, respectively. In particular, we show that is a topological convergence iff forcing by does not produce new reals and that is weakly topological if satisfies condition (implied by the -cc). On the other hand, if is a weakly topological convergence, then is a -cc algebra...
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 Measure for Semialgebraic Sets Related to Boolean Complexity.
A Mixid Theory of Information - IV: Inset-Inaccuracy and Directed Divergence.
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 forcing with ideals and Hechler forcing
A note on indecomposability of Boolean matrices
A note on Möbius inversion over power set lattices
In this paper, we establish a theorem on Möbius inversion over power set lattices which strongly generalizes an early result of Whitney on graph colouring.
A Note On Reproductive Solutions