The axiom of choice has many counterintuitive consequences like the [Banach-Tarski paradox](http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox). 
The Hahn-Banach theorem is a consequence of the axiom of choice, but it is weaker. 


I would like to know some counterintuitive consequences of the Hahn-Banach theorem. 
Can the Banach-Tarski paradox be derived from the Hahn-Banach theorem?



Counterintuitive consequences of the Hahn-Banach theorem
To aid future inquiries, let us record here the go-to reference kindly provided by Willie Wong in a comment above: <http://consequences.emich.edu/conseq.htm>. This provides a data base with a utility to search for known implications between weak forms of the axiom of choice. 


