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Abstract: After Scott, mathematical models of the type-free lambda calculus are constructed by order theoretic methods and classified into semantics according to the nature of their representable functions. Selinger [47] asked if there is a lambda theory that is not induced by any non-trivially partially ordered model (order-incompleteness problem). In terms of Alexandroff topology (the strongest topology whose specialization order is the order of the considered model) the problem of order incompleteness ... (Update)
Context of citations to this paper: More
.... Selinger has recently proven [26] that the term model of fi theory does not admit any non trivial compatible partial order (see also [19, 20]) Plotkin has conjectured [18] that there exists an absolutely unorderable combinatory algebra, that is, a combinatory algebra which...
.... 1 A preliminary version of this result was presented to Workshop on Bohm theorem: applications to Computer Science Theory (BOTH 2001) [28]. 17 Proof: The order incompleteness follows from Thm. 5.1(iii) 2 We now analyse the relationships between the order incompleteness...
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2: Lambda calculus: some models some philosophy (context) - Scott - 1980
2: What Is a Model of the Lambda Calculus (context) - Meyer - 1982
2: a question of H. Friedman (context) - Plotkin - 1996
BibTeX entry: (Update)
Salibra, A., "Towards lambda calculus order-incompleteness", in: J. L'evy (ed.), Workshop on Bohm theorem: applications to Computer Science Theory (BOTH http://citeseer.ist.psu.edu/478984.html More
@inproceedings{ salibra01towards,
author = "Antonino Salibra",
title = "Towards Lambda Calculus Order-Incompleteness",
booktitle = "Workshop on {B}ohm theorem: applications to Computer Science Theory (BOTH 2001)",
series = "Electronic Notes in Theoretical Computer Science",
volume = "50",
number = "2",
year = "2001",
url = "citeseer.ist.psu.edu/478984.html" }
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