### 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

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

# 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