### 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

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

# 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

## 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