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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

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

# 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