### Archives

### Recent blog posts

- 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

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