### 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

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

# 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