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Me and Victor Nascimento just got an article accepted in Analysis!

In the paper, we offer a minor modification to the definition of proof-theoretic validity which makes it a semantics for intuitionistic logic (which the initial definitions surprisingly turned out not to be!)

If you want to read the preprint it is available here: drive.google.com/open?id=1Luhq

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@will Neat. Question: is there an order-theoretic component here? It looks like an atomic system amounts to the presentation of a poset (maybe a semilattice) with a distinguished element ⊥? What I am wondering is whether there's a way to steer into semantics earlier on, and see the result as saying something about ordered structures of a certain kind.

@andrejbauer Something like that sounds right. I don't have a lot of familiarity with algebraic semantics. But a poset with ⊥ would seem like the right structures.

@will Great! It was about time people carried on tackling incompleteness of IPL by making adjustments to the standard PTS definitions. I will definitely take a look.

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