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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

05A17 Forcing Small forcing Cardinal function Erdos Cardinal Hindman's Theorem Uniformization ccc weak square Poset Weakly compact cardinal Diamond Successor of Regular Cardinal Constructible Universe middle diamond P-Ideal Dichotomy Shelah's Strong Hypothesis Prevalent singular cardinals S-Space PFA(S)[S] Singular Density Partition Relations Rado's conjecture Commutative cancellative semigroups Universal Sequences Singular coﬁnality tensor product graph OCA Fast club stationary reflection Antichain b-scale Mandelbrot set Fat stationary set square Stevo Todorcevic HOD Singular cardinals combinatorics Whitehead Problem Minimal Walks Jonsson cardinal free Boolean algebra Selective Ultrafilter Hereditarily Lindelöf space Cohen real 20M14 Chang's conjecture Rainbow sets Successor of Singular Cardinal Singular Cofinality Knaster Hedetniemi's conjecture Ascent Path Dushnik-Miller Sakurai's Bell inequality Coherent tree Rock n' Roll Microscopic Approach Club Guessing Parameterized proxy principle polarized partition relation 11P99 Axiom R Foundations diamond star Large Cardinals Non-saturation Prikry-type forcing projective Boolean algebra L-space PFA very good scale Martin's Axiom Almost-disjoint famiy incompactness Almost Souslin 05D10 Slim tree approachability ideal Chromatic number Forcing Axioms Reduced Power Square-Brackets Partition Relations Kurepa Hypothesis Absoluteness sap reflection principles Ostaszewski square Almost countably chromatic weak diamond Generalized Clubs Erdos-Hajnal graphs Aronszajn tree Souslin Tree stationary hitting Cardinal Invariants

# 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