### Archives

### Recent blog posts

- 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
- Syndetic colorings with applications to S and L October 26, 2013
- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013

### Keywords

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

# 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