### 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

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

# 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