### 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

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

# Tag Archives: Reduced Power

## P.O.I. Workshop in pure and descriptive set theory, September 2015

I gave an invited talk at the P.O.I Workshop in pure and descriptive set theory, Torino, September 26, 2015. Title: $\aleph_3$-trees. Abstract: We inspect the constructions of four quite different $\aleph_3$-Souslin trees.

## 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