Journal ArticleDOI
The shelahP-point independence theorem
TLDR
In this paper, the authors present a model of set theory in which there are noP-points in βN/N and show that this model is consistent with Shelah's example.Abstract:
In this paper, we present S. Shelah's example of a model of set theory in which there are noP-points in βN/N. This settles the famous open question: “Is ‘ZFC+there are noP-points in βN/N’ consistent?”read more
Citations
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Book ChapterDOI
An Introduction to βω
TL;DR: In this article, the authors introduce the space βω, the Stone Space of the Boolean algebra P(ω) of subsets of ω, and show that it is consistent that P-points do not exist in βω/ω.
Book
Proper and Improper Forcing
TL;DR: In this paper, the authors give a complete presentation of the theory of proper forcing and its relatives, starting from the beginning and avoiding the metamathematical considerations, and show methods which can be used for such independence results.
Book ChapterDOI
Combinatorial Cardinal Characteristics of the Continuum
TL;DR: The main results about these cardinal characteristics of the continuum are of two sorts: inequalities involving two (or sometimes three) characteristics, and independence results that other such inequalities cannot be proved in ZFC as discussed by the authors.
Book
Banach Algebras on Semigroups and on Their Compactifications
TL;DR: In this article, the authors studied the structure of the second dual of the semigroup algebra and its amenability constant, showing that there are 'forbidden values' for this constant.
Book ChapterDOI
Weak P-Points in N*
TL;DR: In this article, the points of sN with the non-principal ultrafilters are identified, i.e., points of N* are the points in sN that contain the principal ultra-filters.
References
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Book
The Theory of Ultrafilters
TL;DR: The Rudin-Keisler Order on Types of Ultrafilters as discussed by the authors is a generalization of the Rudin Frolik Order on primitive types of Boolean Algebras.
Journal ArticleDOI
Homogeneity Problems in the Theory of Čech Compactifications
TL;DR: The Cech compactification of a regular topological space is studied in this paper, which is characterized by three properties: sX is a compact Hausdorff space, X is a dense subset of sX, and every bounded continuous real-valued function on X can be extended to a continuous function on βX.
Journal ArticleDOI
Ultrafilters and independent sets
TL;DR: In this article, independent sets are used to show that the Rudin-Keisler ordering on ultra-filters is nonlinear, which is known to be provable from some form of the generalized continuum hypothesis.
Journal ArticleDOI
Combinatorics on ideals and forcing
TL;DR: In this paper, Krivine et al. showed that the minimality of the generic real depends on a combinatorial property of the ideal J on ~, which is a natural generalization of Cohen's set of forcing conditions (the t w ~ valued functions with domain a finite subset of w).