### 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

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

# 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