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- Genearlizations 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
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013

### Keywords

Foundations PFA Shelah's Strong Hypothesis Constructible Universe Successor of Singular Cardinal Prevalent singular cardinals Mandelbrot set OCA Singular cardinals combinatorics L-space incompactness Rock n' Roll Successor of Regular Cardinal Rainbow sets free Boolean algebra Singular Density Hereditarily Lindelöf space tensor product graph Non-saturation PFA(S)[S] S-Space Cohen real Erdos-Hajnal graphs Almost-disjoint famiy Aronszajn tree projective Boolean algebra Cardinal Invariants Ostaszewski square Absoluteness middle diamond polarized partition relation Club Guessing Forcing Axioms Minimal Walks Erdos Cardinal Almost countably chromatic Square-Brackets Partition Relations sap Knaster Kurepa Hypothesis Large Cardinals Small forcing reflection principles Universal Sequences Uniformization Axiom R stationary reflection Hedetniemi's conjecture Antichain P-Ideal Dichotomy Forcing Cardinal function Sakurai's Bell inequality Diamond diamond star Poset square Dushnik-Miller Souslin Tree Rado's conjecture weak square approachability ideal weak diamond ccc Singular Cofinality Martin's Axiom Chromatic number Partition Relations Prikry-type forcing stationary hitting b-scale Weakly compact cardinal very good scale Generalized Clubs Whitehead Problem

# Tag Archives: sap

## Jensen’s diamond principle and its relatives

This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … Continue reading

Posted in Open Problems, Publications
Tagged 03E05, 03E35, 03E50, approachability ideal, Club Guessing, Diamond, diamond star, Non-saturation, sap, Souslin Tree, square, stationary hitting, Uniformization, Whitehead Problem
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## 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

## A relative of the approachability ideal, diamond and non-saturation

Abstract: Let $\lambda$ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square^*_\lambda$ together with $2^\lambda=\lambda^+$ implies $\diamondsuit_S$ for every $S\subseteq\lambda^+$ that reflects stationarily often. In this paper, for a subset $S\subset\lambda^+$, a normal subideal of … Continue reading