### 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

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

# 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