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- 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

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

# 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