A Semantical Analysis of Implicational System I and of the First Degree of Entailment.
A semantical hierarchy for modal formulas.
In this paper a semantical partition, relative to Kripke models, is introduced for sets of formulas. Secondly, this partition is used to generate a semantical hierarchy for modal formulas. In particular some results are given for the propositional calculi T and S4.
A semifilter approach to selection principles
In this paper we develop the semifilter approach to the classical Menger and Hurewicz properties and show that the small cardinal is a lower bound of the additivity number of the -ideal generated by Menger subspaces of the Baire space, and under every subset of the real line with the property is Hurewicz, and thus it is consistent with ZFC that the property is preserved by unions of less than subsets of the real line.
A semifilter approach to selection principles II: -covers
Developing the idea of assigning to a large cover of a topological space a corresponding semifilter, we show that every Menger topological space has the property provided , and every space with the property is Hurewicz provided . Combining this with the results proven in cited literature, we settle all questions whether (it is consistent that) the properties and [do not] coincide, where and run over , , , , and .
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,...