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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

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

# 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