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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

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