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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

Poset Antichain PFA Kurepa Hypothesis sap Distributive tree incompactness Cohen real Almost countably chromatic Chromatic number Erdos-Hajnal graphs L-space Square-Brackets Partition Relations Commutative cancellative semigroups Prevalent singular cardinals Absoluteness Cardinal function Foundations Rock n' Roll Successor of Singular Cardinal Coherent tree Singular cardinals combinatorics Ascent Path stationary reflection Forcing Chang's conjecture weak square Singular Density Almost-disjoint famiy 20M14 square principles Axiom R Parameterized proxy principle Hedetniemi's conjecture Rado's conjecture Diamond OCA coloring number Partition Relations Rainbow sets Fat stationary set Minimal Walks Generalized Clubs P-Ideal Dichotomy Dushnik-Miller reflection principles b-scale Sakurai's Bell inequality Hindman's Theorem very good scale Prikry-type forcing Hereditarily Lindelöf space PFA(S)[S] Fast club Jonsson cardinal Knaster ccc Universal Sequences middle diamond Small forcing weak diamond Shelah's Strong Hypothesis Club Guessing Postprocessing function Uniformization 05A17 Erdos Cardinal Weakly compact cardinal Microscopic Approach polarized partition relation Forcing Axioms Souslin Tree free Boolean algebra Martin's Axiom 11P99 Stevo Todorcevic Reduced Power Constructible Universe 05D10 approachability ideal tensor product graph Large Cardinals Whitehead Problem Fodor-type reflection Nonspecial tree Ostaszewski square Successor of Regular Cardinal HOD stationary hitting Non-saturation Almost Souslin Singular coﬁnality Slim tree Aronszajn tree Selective Ultrafilter square S-Space Cardinal Invariants projective Boolean algebra Mandelbrot set Uniformly coherent xbox diamond star

# 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