### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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