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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

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

# 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