### 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
- Genearlizations 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

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

# 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