### 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

free Boolean algebra weak square middle diamond Commutative cancellative semigroups Constructible Universe Fast club 05D10 Kurepa Hypothesis Mandelbrot set Absoluteness S-Space Uniformization Almost Souslin Forcing Axioms weak diamond Small forcing Diamond square Prikry-type forcing Fat stationary set Sakurai's Bell inequality Cardinal Invariants Weakly compact cardinal Souslin Tree Knaster Erdos Cardinal Cardinal function Almost countably chromatic Whitehead Problem Uniformly coherent ccc Shelah's Strong Hypothesis Square-Brackets Partition Relations L-space Antichain square principles sap Nonspecial tree Foundations Hereditarily Lindelöf space stationary hitting Parameterized proxy principle 05A17 Non-saturation Microscopic Approach Singular coﬁnality HOD Chang's conjecture Reduced Power Rock n' Roll Erdos-Hajnal graphs 11P99 Partition Relations Hedetniemi's conjecture stationary reflection Selective Ultrafilter tensor product graph Fodor-type reflection Jonsson cardinal Universal Sequences very good scale Slim tree Singular Density Coherent tree Distributive tree Singular cardinals combinatorics Ostaszewski square Almost-disjoint famiy approachability ideal b-scale Prevalent singular cardinals Rado's conjecture Postprocessing function PFA(S)[S] coloring number Successor of Singular Cardinal Martin's Axiom diamond star polarized partition relation Hindman's Theorem Dushnik-Miller Poset OCA Stevo Todorcevic 20M14 incompactness Chromatic number Axiom R xbox Rainbow sets Minimal Walks projective Boolean algebra reflection principles P-Ideal Dichotomy Ascent Path Successor of Regular Cardinal Cohen real Aronszajn tree Club Guessing Generalized Clubs Forcing Large Cardinals PFA

# 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