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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

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

# 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