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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

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

# 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