Antonino Salibra (Università Cà Foscari, Venezia, Italy), From Lambda Calculi to Universal Algebra and Topology: Back and Forth



Answering a question by Honsell and Plotkin, we show that there are two equations between lambda terms, the so-called subtractive equations, consistent with lambda calculus but not contemporaneously satisfied in any Scott continuous model.

We also relate the subtractive equations to the open problem of the order-incompleteness of lambda calculus, by studying the connection between the notion of absolute unorderability in a specific point and a weaker notion of subtractivity, namely n-subtractivity, for partially ordered algebras. Finally we study the relation between n-subtractivity and relativized separation conditions in topological algebras, obtaining an incompleteness theorem for a general topological semantics of lambda calculus.