### 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

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

# Tag Archives: Slim tree

## 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