Maximal independent sets, variants of chain/antichain principle and cofinal subsets without AC
In set theory without the axiom of choice (AC), we observe new relations of the following statements with weak choice principles.
Maximal σ-independent families
Maximizing and minimizing fuzzy sets.
Measurability of equivalence classes and MEC-property in metric spaces.
Measurability of functions with approximately continuous vertical sections and measurable horizontal sections
Measurability of some sets of Borel measurable functions on .
Measurable cardinals and analytic games
Measurable cardinals and category bases
We show that the existence of a non-trivial category base on a set of regular cardinality with each subset being Baire is equiconsistent to the existence of a measurable cardinal.
Measurable cardinals and fundamental groups of compact spaces
We prove that all groups can be realized as fundamental groups of compact spaces if and only if no measurable cardinals exist. If the cardinality of a group G is nonmeasurable then the compact space K such that G = π₁K may be chosen so that it is path connected.
Measurable cardinals and the cofinality of the symmetric group
Assuming the existence of a P₂κ-hypermeasurable cardinal, we construct a model of Set Theory with a measurable cardinal κ such that and the group Sym(κ) of all permutations of κ cannot be written as the union of a chain of proper subgroups of length < κ⁺⁺. The proof involves iteration of a suitably defined uncountable version of the Miller forcing poset as well as the “tuning fork” argument introduced by the first author and K. Thompson [J. Symbolic Logic 73 (2008)].
Measurable envelopes, Hausdorff measures and Sierpiński sets
We show that the existence of measurable envelopes of all subsets of ℝⁿ with respect to the d-dimensional Hausdorff measure (0 < d < n) is independent of ZFC. We also investigate the consistency of the existence of -measurable Sierpiński sets.
Measurable Functions and Almost Continuous Functions.
Measurable products of modules
Measurable spaces with c.c.c. [Book]
Measure-additive coverings and measurable selectors [Book]
Measures on Corson compact spaces
We prove that the statement: "there is a Corson compact space with a non-separable Radon measure" is equivalent to a number of natural statements in set theory.
Measure-theoretic unfriendly colorings
We consider the problem of finding a measurable unfriendly partition of the vertex set of a locally finite Borel graph on standard probability space. After isolating a sufficient condition for the existence of such a partition, we show how it settles the dynamical analog of the problem (up to weak equivalence) for graphs induced by free, measure-preserving actions of groups with designated finite generating set. As a corollary, we obtain the existence of translation-invariant random unfriendly colorings...
Medidas de nitidez para conjuntos difusos.
En este trabajo se realiza un estudio de Medidas de Nitidez para conjuntos difusos. Se comienza dando los conceptos de Medida Puntual de Nitidez o Auto-nitidez puntual y Medida de Nitidez para conjunto difuso, pasando a continuación a dar dos teoremas de construcción de Medidas de Nitidez y uno de caracterización para aquellas medidas que sean valoraciones en el retículo Ln(X).
Medium distances of probability-fuzzy points and an application to linear programming
Mengentheoretische Modelle des ...K-Kalküls.