### 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

Selective Ultrafilter Rainbow sets diamond star Shelah's Strong Hypothesis Successor of Singular Cardinal PFA(S)[S] Almost-disjoint famiy Microscopic Approach Sakurai's Bell inequality Poset Jonsson cardinal Forcing Commutative cancellative semigroups Non-saturation Forcing Axioms Erdos Cardinal Hereditarily Lindelöf space Singular Cofinality Fodor-type reflection Rado's conjecture Ascent Path sap incompactness Slim tree Foundations 11P99 Prevalent singular cardinals 05D10 approachability ideal weak diamond middle diamond Hindman's Theorem Constructible Universe P-Ideal Dichotomy Square-Brackets Partition Relations Cardinal function free Boolean algebra Successor of Regular Cardinal stationary reflection Hedetniemi's conjecture Diamond Almost countably chromatic Large Cardinals projective Boolean algebra Stevo Todorcevic Club Guessing Chromatic number Kurepa Hypothesis L-space Dushnik-Miller 20M14 weak square xbox Rock n' Roll polarized partition relation tensor product graph Souslin Tree Cohen real S-Space Mandelbrot set Parameterized proxy principle 05A17 square PFA Singular coﬁnality Chang's conjecture Fast club coloring number Uniformization Ostaszewski square Small forcing Axiom R HOD b-scale Singular Density Absoluteness Aronszajn tree Reduced Power very good scale Minimal Walks Fat stationary set reflection principles stationary hitting Weakly compact cardinal ccc square principles Partition Relations Universal Sequences Erdos-Hajnal graphs Almost Souslin Singular cardinals combinatorics Generalized Clubs OCA Coherent tree Prikry-type forcing Antichain Martin's Axiom Cardinal Invariants Knaster Whitehead Problem

# 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