### 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

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

# Tag Archives: Fast club

## Prikry forcing may add a Souslin tree

A celebrated theorem of Shelah states that adding a Cohen real introduces a Souslin tree. Are there any other examples of notions of forcing that add a $\kappa$-Souslin tree? and why is this of interest? My motivation comes from a … Continue reading