### 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

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

# Tag Archives: 05C05

## A Microscopic approach to Souslin-tree constructions. Part I

Joint work with Ari Meir Brodsky. Abstract. We propose a parameterized proxy principle from which $\kappa$-Souslin trees with various additional features can be constructed, regardless of the identity of $\kappa$. We then introduce the microscopic approach, which is a simple … Continue reading

Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E65, 05C05, Coherent tree, Diamond, Microscopic Approach, Parameterized proxy principle, Slim tree, Souslin Tree, square, xbox
4 Comments

## 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