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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

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

# 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