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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

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

# 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