The 0-distributivity in the class of subalgebra lattices of Heyting algebras and closure algebras
The Countable Chain Condition and Free Algebras.
The distributivity numbers of finite products of P(ω)/fin
Generalizing [ShSp], for every n < ω we construct a ZFC-model where ℌ(n), the distributivity number of r.o., is greater than ℌ(n+1). This answers an old problem of Balcar, Pelant and Simon (see [BaPeSi]). We also show that both Laver and Miller forcings collapse the continuum to ℌ(n) for every n < ω, hence by the first result, consistently they collapse it below ℌ(n).
The elementary-equivalence classes of clopen algebras of P-spaces
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.
The equivalence of Boolean prime ideal theorem and a theorem of functional analysis
The lattice of subvarieties of the biregularization of the variety of Boolean algebras
Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V). Let B be the variety of Boolean algebras of type , where and . In...
The semigroup of circulant Boolean matrices
Two properties of free Boolean algebras
Two theorems of functional analysis effectively equivalent to choice axioms