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### Recent blog posts

- 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
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013

### Keywords

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

# 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