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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
- Generalizations 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

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

# 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