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### 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
- 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

### Keywords

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

# 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