Borel Conjecture and Dual Borel Conjecture

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.Comment: 47 pages, revised version 2013 (some typos removed, some points elaborated. Dedication added.

Session Types in Abelian Logic

There was a PhD student who says "I found a pair of wooden shoes. I put a coin in the left and a key in the right. Next morning, I found those objects in the opposite shoes." We do not claim existence of such shoes, but propose a similar programming abstraction in the context of typed lambda calculi. The result, which we call the Amida calculus, extends Abramsky's linear lambda calculus LF and characterizes Abelian logic.Comment: In Proceedings PLACES 2013, arXiv:1312.221