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### 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

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