### 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

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

# 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