Is there any research activity going on in the field of proof theory today? If so, what are some of the most active areas, what types of questions do they deal with, and where can I go to find out more about them? I'm concerned more with the logic side of this question than the mathematical one.
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You can see some recent books like: Helmut Schwichtenberg & Stanley Wainer, Proofs and Computations (2012) and: Sara Negri & Jan von Plato, Proof Analysis: A Contribution to Hilbert’s Last Problem (2011). – Mauro ALLEGRANZA May 21 '16 at 17:47
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Maybe linear logic, en.wikipedia.org/wiki/Linear_logic , and substructural logics, en.wikipedia.org/wiki/Substructural_logic , in general. Or maybe go to the homepages of any well-known proof theorists, e.g., iml.univ-mrs.fr/~girard (you might want google to translate that for you), and see what they've been publishing recently. – John Forkosh May 25 '16 at 7:36
