### Archives

### 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

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

# Tag Archives: Generalized Clubs

## 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

## On guessing generalized clubs at the successors of regulars

Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading