### 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

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

# 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