### 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

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

# 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
1 Comment

## 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