On positive, linear and quadratic Boolean functions
On preimages of ultrafilters in ZF
We show that given infinite sets and a function which is onto and -to-one for some , the preimage of any ultrafilter of under extends to an ultrafilter. We prove that the latter result is, in some sense, the best possible by constructing a permutation model with a set of atoms and a finite-to-one onto function such that for each free ultrafilter of its preimage under does not extend to an ultrafilter. In addition, we show that in there exists an ultrafilter compact pseudometric...
On Priestley duals of products
On rings satisfying certain polynomial identities.
On Semi-Boolean-Like Algebras
In a previous paper, we introduced the notion of Boolean-like algebra as a generalisation of Boolean algebras to an arbitrary similarity type. In a nutshell, a double-pointed algebra with constants is Boolean-like in case for all the congruences and are complementary factor congruences of . We also introduced the weaker notion of semi-Boolean-like algebra, showing that it retained some of the strong algebraic properties characterising Boolean algebras. In this paper, we continue the investigation...
On semigroups of Boolean ring endomorphisms.
On semigroups of -endomorphisms
On set-valued non-Boolean functions.
On some connections between Boolean algebras and Heyting algebras
On some numerical characterization of Boolean algebras
On Some Relations in Boolean Algebras
On some types of radical classes
Let be an infinite cardinal. We denote by the collection of all -representable Boolean algebras. Further, let be the collection of all generalized Boolean algebras such that for each , the interval of belongs to . In this paper we prove that is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered groups and generalized -algebras.
On the algebraic structure of the process of forming subsequences
On the Automorphism Groups of Denumerable Boolean Algebras.
On the cardinality and weight spectra of compact spaces, II
Let B(κ,λ) be the subalgebra of P(κ) generated by . It is shown that if B is any homomorphic image of B(κ,λ) then either or ; moreover, if X is the Stone space of B then either or . This implies the existence of 0-dimensional compact spaces whose cardinality and weight spectra omit lots of singular cardinals of “small” cofinality.
On the compactification of closure algebras
On the existence of prime ideals in Boolean algebras
Rasiowa and Sikorski [5] showed that in any Boolean algebra there is an ultrafilter preserving countably many given infima. In [3] we proved an extension of this fact and gave some applications. Here, besides further remarks, we present some of these results in a more general setting.
On the implementation of set-valued non-Boolean functions.
On the injectivity of Boolean algebras
The functor taking global elements of Boolean algebras in the topos of sheaves on a complete Boolean algebra is shown to preserve and reflect injectivity as well as completeness. This is then used to derive a result of Bell on the Boolean Ultrafilter Theorem in -valued set theory and to prove that (i) the category of complete Boolean algebras and complete homomorphisms has no non-trivial injectives, and (ii) the category of frames has no absolute retracts.
On the lattice of subalgebras of a Boolean algebra