### 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

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

# 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