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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
- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
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weak square Aronszajn tree incompactness Generalized Clubs Forcing Knaster Singular cardinals combinatorics sap Almost Souslin Forcing Axioms Hindman's Theorem HOD Small forcing Singular Cofinality Dushnik-Miller approachability ideal Chromatic number Constructible Universe projective Boolean algebra Microscopic Approach reflection principles Mandelbrot set Commutative cancellative semigroups Cohen real Ascent Path Coherent tree Uniformization Partition Relations Martin's Axiom Large Cardinals 11P99 Ostaszewski square Hereditarily Lindelöf space stationary reflection OCA weak diamond Fat stationary set Universal Sequences Prikry-type forcing b-scale Cardinal function 20M14 Absoluteness Souslin Tree Cardinal Invariants Diamond S-Space Singular coﬁnality Successor of Singular Cardinal Shelah's Strong Hypothesis Hedetniemi's conjecture Whitehead Problem Club Guessing tensor product graph diamond star Slim tree Prevalent singular cardinals polarized partition relation Kurepa Hypothesis free Boolean algebra Foundations Non-saturation Fast club Almost countably chromatic P-Ideal Dichotomy Almost-disjoint famiy PFA Antichain Weakly compact cardinal ccc Minimal Walks square Successor of Regular Cardinal Axiom R L-space Poset middle diamond Sakurai's Bell inequality Reduced Power very good scale Selective Ultrafilter Stevo Todorcevic Rock n' Roll Erdos-Hajnal graphs Rado's conjecture PFA(S)[S] Singular Density Parameterized proxy principle Erdos Cardinal 05A17 05D10 Rainbow sets Square-Brackets Partition Relations stationary hitting

# 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 Preprints, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, square
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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