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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

### Keywords

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

# Tag Archives: diamond star

## Square with built-in diamond-plus

Joint work with Ralf Schindler. Abstract. We formulate combinatorial principles that combine the square principle with various strong forms of diamond, and prove that the strongest amongst them holds in $L$ for every infinite cardinal. As an application, we prove that … Continue reading

Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, square, xbox
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## A Kurepa tree from diamond-plus

Recall that $T$ is said to be a $\kappa$-Kurepa tree if $T$ is a tree of height $\kappa$, whose levels $T_\alpha$ has size $\le|\alpha|$ for co-boundedly many $\alpha<\kappa$, and such that the set of branches of $T$ has size $>\kappa$. … Continue reading

## 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

## 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