### 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

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

# Tag Archives: Coherent 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