### 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

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

# Tag Archives: Ascent Path

## 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