Invariant sets in topology and logic
Invariant uniformization
Involutions in fuzzy set theory.
All possible involutions in fuzzy set theory are completely described. Any involution is a composition of a symmetry on a universe of fuzzy sets and an involution on a truth set.
Irreducible images of
Is the product of ccc spaces a ccc space?
In this expository paper it is shown that Martin's Axiom and the negation of the Continuum Hypothesis imply that the product of ccc spaces is a ccc space. The Continuum Hypothesis is then used to construct the Laver-Gavin example of two ccc spaces whose product is not a ccc space.
It is consistent that there exists an ordered real closed field which is not hyper-real.
Iterated products of ideals of Borel sets
Iterated ultrapower and Prikry's forcing
Iterating along a Prikry sequence
We introduce a new method which combines Prikry forcing with an iteration between the Prikry points. Using our method we prove from large cardinals that it is consistent that the tree property holds at ℵₙ for n ≥ 2, is strong limit and .
Iteration of -complete forcing notions not collapsing .
Joins of congruences in -groups
Juegos no cooperativos con preferencias difusas.
El objetivo de este trabajo es el estudio de los juegos no cooperativos en los que los jugadores expresan sus preferencias sobre las consecuencias que se derivan de sus acciones mediante relaciones binarias difusas. El concepto de solución que se maneja es el de estrategias en equilibrio. La existencia de tales estrategias queda probada en el caso de que los jugadores definan sus preferencias sobre las consecuencias aleatorias mediante la extensión lineal introducida en Montero-Tejada (1986a).
-common consequents in Boolean matrices
-bounded sets and filters on
Kappa-Slender Modules
For an arbitrary infinite cardinal , we define classes of -cslender and -tslender modules as well as related classes of -hmodules and initiate a study of these classes.
Kategorielle Mengenlehre: Eine Charakterisierung der Kategorie der Klassen und Abbildungen.
Keeping the covering number of the null ideal small
It is proved that ideal-based forcings with the side condition method of Todorcevic (1984) add no random reals. By applying Judah-Repický's preservation theorem, it is consistent with the covering number of the null ideal being ℵ₁ that there are no S-spaces, every poset of uniform density ℵ₁ adds ℵ₁ Cohen reals, there are only five cofinal types of directed posets of size ℵ₁, and so on. This extends the previous work of Zapletal (2004).
Kelley's specialization of Tychonoff's Theorem is equivalent to the Boolean Prime Ideal Theorem
The principle that "any product of cofinite topologies is compact" is equivalent (without appealing to the Axiom of Choice) to the Boolean Prime Ideal Theorem.
Killing GCH everywhere by a cofinality-preserving forcing notion over a model of GCH
Starting from large cardinals we construct a pair V₁⊆ V₂ of models of ZFC with the same cardinals and cofinalities such that GCH holds in V₁ and fails everywhere in V₂.