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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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