[FOM] paper: Partial Combinatory Algebras of Functions

[Jaap van Oosten]

A new paper of mine is available on the Arxiv:

http://front.math.ucdavis.edu/0905.2665

*Abstract:* 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 J. 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 quotient of a realizability topos on a 
total combinatory algebra.