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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

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

# 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