### Archives

### Recent blog posts

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

# Tag Archives: Almost Souslin

## 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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## Reduced powers of Souslin trees

Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading