Linear logic isn't complete for coherence space semantics since $1$ and $\top$ get identified. But it is, I believe, complete for the fragment of linear logic whose only connective is $\multimap$.I was wondering if there's a full completeness result for theories in the fragment of linear logic whose only connective is $\multimap$? I think this is equivalent to asking: is the term model of $\lambda$ terms whose variables only get bound exactly once (over some signature, modulo $=_{\eta\beta}$) a coherence space? Since the system I'm interested in is very limited, I was also wondering if there are any simpler structures for which full completeness holds?
Coherence spaces and full completeness for the implicative fragment of linear logic
lo.logic;type theory;typed lambda calculus;linear logic