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 simultaneously satisfied in any partially ordered model with bottom element. 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.

Source : oai:arXiv.org:1311.1916

DOI : 10.2168/LMCS-9(4:21)2013

Volume: Volume 9, Issue 4

Published on: December 12, 2013

Submitted on: January 24, 2013

Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic

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