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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
- Genearlizations 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

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

# 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