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- 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

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

# 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