### 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

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

# 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