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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

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

# 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