### Archives

### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations 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

### Keywords

Mandelbrot set Selective Ultrafilter 20M14 Microscopic Approach b-scale 11P99 Constructible Universe Axiom R Prikry-type forcing stationary reflection coloring number PFA(S)[S] Sakurai's Bell inequality Weakly compact cardinal Cardinal Invariants Rock n' Roll Antichain xbox Cardinal function Ascent Path middle diamond Chang's conjecture Universal Sequences Hindman's Theorem Souslin Tree Kurepa Hypothesis Forcing Axioms Square-Brackets Partition Relations Coherent tree approachability ideal Fast club Almost Souslin Commutative cancellative semigroups Shelah's Strong Hypothesis Rado's conjecture ccc square Slim tree Nonspecial tree OCA Partition Relations Singular cardinals combinatorics tensor product graph Generalized Clubs P-Ideal Dichotomy square principles Distributive tree Minimal Walks polarized partition relation sap diamond star Poset Almost countably chromatic Fat stationary set Successor of Regular Cardinal Successor of Singular Cardinal Singular coﬁnality Hereditarily Lindelöf space projective Boolean algebra weak square Postprocessing function Absoluteness stationary hitting Cohen real incompactness 05A17 Dushnik-Miller Singular Density Diamond Martin's Axiom Non-saturation weak diamond free Boolean algebra Large Cardinals Hedetniemi's conjecture Prevalent singular cardinals Aronszajn tree Forcing Stevo Todorcevic Jonsson cardinal Club Guessing Chromatic number very good scale Reduced Power Knaster Parameterized proxy principle L-space Uniformly coherent HOD Rainbow sets reflection principles super-Souslin tree Erdos Cardinal S-Space Almost-disjoint famiy Ostaszewski square Whitehead Problem Fodor-type reflection Small forcing Foundations PFA Uniformization Erdos-Hajnal graphs Luzin set

# 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