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### 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

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

# 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