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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

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

# 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