Open Access
2011 Partial Combinatory Algebras of Functions
Jaap van Oosten
Notre Dame J. Formal Logic 52(4): 431-448 (2011). DOI: 10.1215/00294527-1499381


We employ the notions of "sequential function" and "interrogation" (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using Longley's preorder-enriched category of partial combinatory algebras and decidable applicative structures. We also investigate total combinatory algebras of partial functions. One of the results is that every realizability topos is a geometric quotient of a realizability topos on a total combinatory algebra.


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Jaap van Oosten. "Partial Combinatory Algebras of Functions." Notre Dame J. Formal Logic 52 (4) 431 - 448, 2011.


Published: 2011
First available in Project Euclid: 4 November 2011

zbMATH: 1248.03026
MathSciNet: MR2855881
Digital Object Identifier: 10.1215/00294527-1499381

Primary: 03B40
Secondary: 68N18

Keywords: partial combinatory algebra , preorder enriched category , sequential function

Rights: Copyright © 2011 University of Notre Dame

Vol.52 • No. 4 • 2011
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