Abstract:
let c reg be a non-empty class (of regular cardinals). then the logic has additional nice properties: it has the homogeneous model existence property.

Abstract:
Let C Reg be a non-empty class (of regular cardinals). Then the logic has additional nice properties: it has the homogeneous model existence property. Sea C Reg una clase no vacía (de cardinales regulares). Entonces la lógica tiene propiedades adicionales: Esta tiene la propiedad de modelo existencia homogénea.

Abstract:
This paper deals with variety of problems in pcf theory and infinitary combinatorics. We look at normal filters and prc, measures of the size of [lambda]^{ with |B_i|

Abstract:
We are interested in generalizing part of the theory of ultrafilters on omega to larger cardinals. Here we set the scene for further investigations introducing properties of ultrafilters in strong sense dual to being normal.

Abstract:
We strengthen the revised GCH theorem by showing, e.g., that for lambda=cf(lambda)>beth_omega, for all but finitely many regular kappabeth_omega implies the diamond on lambda is restricted to cofinality kappa for all but finitely many kappa in Reg cap beth_omega and we strengthen the results on the middle diamond. Moreover, we get stronger results on the middle diamond.

Abstract:
We show in ZFC, that the depth of ultraproducts of Boolean Algebras may be bigger than the ultraproduct of the depth of those Boolean Algebras.

Abstract:
A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being dependent. Another one justifies the cofinality restriction in the theorem (from a previous work) saying that pairwise perpendicular indiscernible sequences, can have arbitrary dual-cofinalities in some models containing them.

Abstract:
We to a large extent sort out when does a (first order complete theory) T have a superlimit model in a cardinal lambda . Also we deal with relation notions of being limit.

Abstract:
For a dependent theory T, in C_T for every type definable group G, the intersection of type definable subgroups with bounded index is a type definable subgroup with bounded index.

Abstract:
We mainly investigate model of set theory, e.g., ZF + DC + "the family of countable subsets of lambda is well ordered for every lambda" (really local version for a given lambda). In this frame much of pcf theory can be generalized. E.g., there is a class of regular cardinals, and we can prove cardinal inequality.