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

# 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