• Cardinal Invariants of the Continuum

    A few new cardinal invarinats of the continuum are found in Rules and Reals ps, dvi

  • Convexity Theory

    In this paper uncountably many nonconvexity degrees are distinguished among closed subsets of the plane: Degrees of Nonconvexity in the plane ps , dvi .

    And in this one, the same is done in all other dimensions Ranks of nonconvexity in higher Dimension ps , dvi ,

  • PCF theory and Infinite Combinatorics

    A version of the ABC of pcf from 1995 is here ps , dvi . A complete treatment of club-guessing and Shelah's ideal I[Lambda] is found here and the fundamentals of pcf theory up to the existence of generators for pcf (the "pcf theorem"). More to come in this millenium.

    Anothe entrance into pcf theory is the following paper on Exact Upper Bounds ps , dvi . It contains a proof of Shelah's trichotomy theorem for increasing sequences of ordinal fuctions and an extension: a necessary and sufficient condition for the existence of an eub with given limit.

    A complementary counterexample to Shelah's Trichotomy Theorem is in The PCF Trichotomy Theorem does not hold for short sequences ps, dvi

    An application of the Trichotomy to collapse algebras is in Fallen Cardinals ps, dvi

    A construction of a countably complete Souslin tree on aleph two from a non reflecting stationary set of countably cofinal elements Souslin Trees ps , dvi

    Shelah's polarized partition on strong limits of uncountable cofinality Shelah's partition theorem ps , dvi

  • Ramsey Theory

    This short paper contains an elementary proof of the fact that regressive Ramsey numbers for pair colorings grow as fast as the Ackermann function. This is the only variant of Ramsey numbers for pair colorings which produces Ackermannian growth. Regressive Ramsey Numbers ps , dvi .

  • Topology

    A Dowker space is a normal Hausdorff space whose product with the closed unit interval is not normal. These spaces are hot stuff (apparently). Here is the first one whose cardinality, weight and charachter are determined in ZFC. With pcf theory, it is possible to prove that there is a Dowker space of cardinality Aleph_{omega_1}, same weight as cardinality and charachter Aleph_omega}. A ZFC Dowker space from pcf theory ps , dvi

  • Universal Models and Embeddability

    The first paper in which Aleph_2 combinatorics was used to show that non GCH cardinal arithmetic can determine the existence of universals in this Universal Linear Orders ps , dvi . In it there are results about first order theories, linear orders and theoris with the strict order property.

    Similar results are about Stable not superstable Theories ps , dvi , Infinite Abelian Groups ps , dvi

    The following paper deals with a class of graphs in which the relation of embeddability admits a representation as set inclusion Representing Embeddability as Set Inclusion ps , dvi . An easy criterion for consistency of no universals in classes of graphs is in A criterion for unbounded complexity ps , dvi.