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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

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

# 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