### 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
- Genearlizations 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

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

# 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