A space is said to have the Rothberger property (or simply is Rothberger) if for every sequence of open covers of , there exists for each such that . For any , necessary and sufficient conditions are obtained for to have the Rothberger property when is a Mrówka mad family and, assuming CH (the Continuum Hypothesis), we prove the existence of a maximal almost disjoint family for which the space is Rothberger for all .
Let be the strings of fuzzy sets over , where is a finite universe of discourse. We present the algorithms for operations on fuzzy sets and the polynomial time algorithms to find the string over which is a closest common subsequence of fuzzy sets of and using different operations to measure a similarity of fuzzy sets.
In this note, we show that the model obtained by finite support iteration of a sequence of generic extensions of models of ZFC of length is sometimes the smallest common extension of this sequence and very often it is not.
We show the consistency of the statement: "the set of regular cardinals which are the characters of ultrafilters on ω is not convex". We also deal with the set of π-characters of ultrafilters on ω.
Let χ be the minimum cardinality of a subset of that cannot be made convergent by multiplication with a single Toeplitz matrix. By an application of a creature forcing we show that < χ is consistent. We thus answer a question by Vojtáš. We give two kinds of models for the strict inequality. The first is the combination of an ℵ₂-iteration of some proper forcing with adding ℵ₁ random reals. The second kind of models is obtained by adding δ random reals to a model of for some δ ∈ [ℵ₁,κ). It...
Recently, the parameter estimations for normal fuzzy variables in the Nahmias’ sense was studied by Cai [4]. These estimates were also studied for general -related, but not necessarily normal fuzzy variables by Hong [10] In this paper, we report on some properties of estimators that would appear to be desirable, including unbiasedness. We also consider asymptotic or “large-sample” properties of a particular type of estimator.
We show that Martin’s conjecture on Π¹₁ functions uniformly -order preserving on a cone implies Π¹₁ Turing Determinacy over ZF + DC. In addition, it is also proved that for n ≥ 0, this conjecture for uniformly degree invariant functions is equivalent over ZFC to -Axiom of Determinacy. As a corollary, the consistency of the conjecture for uniformly degree invariant Π¹₁ functions implies the consistency of the existence of a Woodin cardinal.
We investigate the reverse mathematical strength of Turing determinacy up to Σ₅⁰, which is itself not provable in second order arithmetic.
We prove a structure theorem asserting that each superflat graph is tree-decomposable in a very nice way. As a consequence we fully determine the spectrum functions of theories of superflat graphs.