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### 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

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

# 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