A semigroup in function algebra.
A sentence that is difficult to interpret
A sequence of theories for arithmetic whose union is complete
A sequential approach to a construction of measures
A set-theoretical equivalent of the prime ideal theorem for Boolean algebras
A short note on lattices allowing disjunctive reasoning.
This short note shows that the scheme of disjunctive reasoning, a or b, not b : a, does not hold neither in proper ortholattices nor in proper de Morgan algebras. In both cases the scheme, once translated into the inequality b' · (a+b) ≤ a, forces the structure to be a boolean algebra.
A short note on representation of L-fuzzy sets by Moore's families.
A short proof of a partion relation for triples.
A simple detailed proof for Goedel's incompleteness theorem
A simple proof that determinacy implies Lebesgue measurability.
A simple tree and its application to a counterexample of Philips.
A simpler set of axioms for polyadic algebras
A solution of a problem of B. Rotman
A solution of a problem of B. Rotman
A solution to Comfort's question on the countable compactness of powers of a topological group
In 1990, Comfort asked Question 477 in the survey book “Open Problems in Topology”: Is there, for every (not necessarily infinite) cardinal number , a topological group G such that is countably compact for all cardinals γ < α, but is not countably compact? Hart and van Mill showed in 1991 that α = 2 answers this question affirmatively under . Recently, Tomita showed that every finite cardinal answers Comfort’s question in the affirmative, also from . However, the question has remained...
A space C(K) where all nontrivial complemented subspaces have big densities
Using the method of forcing we prove that consistently there is a Banach space (of continuous functions on a totally disconnected compact Hausdorff space) of density κ bigger than the continuum where all operators are multiplications by a continuous function plus a weakly compact operator and which has no infinite-dimensional complemented subspaces of density continuum or smaller. In particular no separable infinite-dimensional subspace has a complemented superspace of density continuum or smaller,...
A spectral theorem for MV-algebras
MV-algebras were introduced by Chang, 1958 as algebraic bases for multi-valued logic. MV stands for “multi-valued" and MV algebras have already occupied an important place in the realm of nonstandard (mathematical) logic applied in several fields including cybernetics. In the present paper, using the Loomis–Sikorski theorem for -MV-algebras, we prove that, with every element in a -MV algebra , a spectral measure (i. e. an observable) can be associated, where denotes the Boolean -algebra...
A spectral theory for order unit spaces
A splitting theorem for ℱ-products
A stabilization property and its applications in the theory of sections