### 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

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

# 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