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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

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

# Tag Archives: very good scale

## 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