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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

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

# 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