A connection between Computer Science and Fuzzy Theory: Midpoints and running time of computing.
A consistency result on weak reflection
A constructive proof of the Tychonoff's theorem for locales
A continuum of totally incomparable hereditarily indecomposable Banach spaces
A family is constructed of cardinality equal to the continuum, whose members are totally incomparable hereditarily indecomposable Banach spaces.
A contour view on uninorm properties
Any given increasing function is completely determined by its contour lines. In this paper we show how each individual uninorm property can be translated into a property of contour lines. In particular, we describe commutativity in terms of orthosymmetry and we link associativity to the portation law and the exchange principle. Contrapositivity and rotation invariance are used to characterize uninorms that have a continuous contour line.
A contribution to topology in AST: Almost indiscernibilities
A contribution to topology in AST: Compactness
A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube
We compare the forcing-related properties of a complete Boolean algebra with the properties of the convergences (the algebraic convergence) and on generalizing the convergence on the Cantor and Aleksandrov cube, respectively. In particular, we show that is a topological convergence iff forcing by does not produce new reals and that is weakly topological if satisfies condition (implied by the -cc). On the other hand, if is a weakly topological convergence, then is a -cc algebra...
A Corson compact L-space from a Suslin tree
The completion of a Suslin tree is shown to be a consistent example of a Corson compact L-space when endowed with the coarse wedge topology. The example has the further properties of being zero-dimensional and monotonically normal.
A countable dense homogeneous set of reals of size ℵ₁
We prove there is a countable dense homogeneous subspace of ℝ of size ℵ₁. The proof involves an absoluteness argument using an extension of the logic obtained by adding predicates for Borel sets.
A deceptive fact about functions
The paper provides a proof of a combinatorial result which pertains to the characterization of the set of equations which are solvable in the composition monoid of all partial functions on an infinite set.
A descriptive view of unitary group representations
In this paper, we will study the relative complexity of the unitary duals of countable groups. In particular, we will explain that if and are countable amenable non-type I groups, then the unitary duals of and are Borel isomorphic.
A dichotomy for P-ideals of countable sets
A dichotomy concerning ideals of countable subsets of some set is introduced and proved compatible with the Continuum Hypothesis. The dichotomy has influence not only on the Suslin Hypothesis or the structure of Hausdorff gaps in the quotient algebra / but also on some higher order statements like for example the existence of Jensen square sequences.
A dichotomy theorem for mono-unary algebras
We study the isomorphism relation of invariant Borel classes of countable mono-unary algebras and prove a strong dichotomy theorem.
A discussion on aggregation operators
It has been lately made very clear that aggregation processes can not be based upon a unique binary operator. Global aggregation operators have been therefore introduced as families of aggregation operators , being each one of these the -ary operator actually amalgamating information whenever the number of items to be aggregated is . Of course, some mathematical restrictions can be introduced, in order to assure an appropriate meaning, consistency and key mathematical capabilities. In this...
A few topological problems
A fine hierarchy of partition cardinals
A fixed point theorem equivalent to the axiom of choice.
A forcing construction of thin-tall Boolean algebras
It was proved by Juhász and Weiss that for every ordinal α with there is a superatomic Boolean algebra of height α and width ω. We prove that if κ is an infinite cardinal such that and α is an ordinal such that , then there is a cardinal-preserving partial order that forces the existence of a superatomic Boolean algebra of height α and width κ. Furthermore, iterating this forcing through all , we obtain a notion of forcing that preserves cardinals and such that in the corresponding generic...