The Hahn-Banach theorem implies the existence of a non-Lebesgue measurable set
The Hahn-Banach Theorem surveyed [Book]
The homomorphic images of infinite symmetric groups.
The Hurewicz covering property and slaloms in the Baire space
According to a result of Kočinac and Scheepers, the Hurewicz covering property is equivalent to a somewhat simpler selection property: For each sequence of large open covers of the space one can choose finitely many elements from each cover to obtain a groupable cover of the space. We simplify the characterization further by omitting the need to consider sequences of covers: A set of reals X has the Hurewicz property if, and only if, each large open cover of X contains a groupable subcover. This...
The ideal (a) is not generated
We prove that the ideal (a) defined by the density topology is not generated. This answers a question of Z. Grande and E. Strońska.
The internal and external aspect of logic and set theory in elementary topoi
The internal rate of return of fuzzy cash flows.
An internal rate of return (IRR) of an investment or financing project with cash flow (a0,a1,a2,...,an) is usually defined as a rate of interest r such thata0 + a1(1 + r)-1 + ... + an(1 + r)-n = 0.If the cash flow has one sign change then the previous equation has a unique solution r > -1.Generally the IRR technique does not extend to fuzzy cash flows, as it can be seen with examples (see [2]). In this paper we show that under suitable hypothesis a unique fuzzy IRR exists for a fuzzy cash...
The interpreted type-free modal calculus
The interpreted type-free modal calculus
The interpreted type-free modal calculus . II
The isomorphism relation between tree-automatic Structures
An ω-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for ω-tree-automatic structures. We prove first that the isomorphism relation for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n ≥ 2) is not determined by the axiomatic system ZFC. Then we prove that...
The isomorphism relation on countable torsion free abelian groups
The isomorphism relation on countable torsion free abelian groups is non-Borel.
The lattice of indiscernibility equivalences
The linear refinement number and selection theory
The linear refinement number is the minimal cardinality of a centered family in such that no linearly ordered set in refines this family. The linear excluded middle number is a variation of . We show that these numbers estimate the critical cardinalities of a number of selective covering properties. We compare these numbers to the classical combinatorial cardinal characteristics of the continuum. We prove that = = in all models where the continuum is at most ℵ₂, and that the cofinality of is...
The maximal regular ideal of the semigroup of binary relations
The measure algebra does not always embed
The Open Colouring Axiom implies that the measure algebra cannot be embedded into P(ℕ)/fin. We also discuss errors in previous results on the embeddability of the measure algebra.
The midpoint set of a Cantor set.
The nonabsolute boundedness model of the theory of semisets
The nonexistence of robust codes for subsets of ω₁
Several results are presented concerning the existence or nonexistence, for a subset S of ω₁, of a real r which works as a robust code for S with respect to a given sequence of pairwise disjoint stationary subsets of ω₁, where “robustness” of r as a code may either mean that whenever each is equal to modulo nonstationary changes, or may have the weaker meaning that for every club C ⊆ ω₁. Variants of the above theme are also considered which result when the requirement that S gets exactly...
The non-existence of well-orderings of the Cantor set