### Archives

### Recent blog posts

- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013

### Keywords

Minimal Walks Constructible Universe Successor of Regular Cardinal Cohen real Rado's conjecture Non-saturation stationary hitting Dushnik-Miller Small forcing very good scale projective Boolean algebra L-space PFA(S)[S] Almost-disjoint famiy Shelah's Strong Hypothesis Diamond Forcing Rainbow sets P-Ideal Dichotomy weak square Prevalent singular cardinals Square-Brackets Partition Relations Prikry-type forcing Martin's Axiom Selective Ultrafilter Weakly compact cardinal Cardinal Invariants Kurepa Hypothesis Almost countably chromatic Generalized Clubs Whitehead Problem Sakurai's Bell inequality Microscopic Approach reflection principles Knaster Large Cardinals Almost Souslin middle diamond Partition Relations S-Space incompactness Ostaszewski square Hereditarily Lindelöf space Uniformization Antichain sap approachability ideal square OCA weak diamond b-scale Reduced Power Mandelbrot set free Boolean algebra Aronszajn tree Singular cardinals combinatorics Rock n' Roll Erdos Cardinal PFA Chromatic number Successor of Singular Cardinal ccc Singular Cofinality Souslin Tree Poset Cardinal function Club Guessing Axiom R stationary reflection tensor product graph Erdos-Hajnal graphs Singular Density diamond star Universal Sequences polarized partition relation Hedetniemi's conjecture Foundations Forcing Axioms Absoluteness Ascent Path

# Tag Archives: Generalized Clubs

## The failure of diamond on a reflecting stationary set

Joint work with Moti Gitik. Abstract: It is shown that the failure of $\diamondsuit_S$, for a subset $S\subseteq\aleph_{\omega+1}$ that reflects stationarily often, is consistent with GCH and $\text{AP}_{\aleph_\omega}$, relatively to the existence of a supercompact cardinal. This should be comapred with … Continue reading

## On guessing generalized clubs at the successors of regulars

Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading