HDS28: Bethke, Ingemarie (2018) Notes on Partial Combinatory Algebras. Doctoral thesis, University of Amsterdam.
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Abstract
This dissertation is a collection of five loosely connected papers on various subjects within the framework of socalled combinatorial algebras, ie. models of combinatorial logic. The articles are preceded by a general introduction and a brief survey of some of the basic notions for combinatory algebras.
In chapter 3 we present a construction method for extensional combinatory algebras based on probably the simplest known model construction, the graph model D_A. This construction is based on the technique of the extensional collapse.
In chapter 4 we modify this approach in order to construct nontotal extensional combinatorial algebras. We introduce the notion of a preflexive complete partial order and describe a construction method for such structions. The final section of chapter 4 comprises some properties of the models constructed in this way.
Chapter 5 deals with cardinality aspects of topological models; in particular, it is shown that nontotal topological combinatorial algebras are uncountable.
In chapter 6 we show that every partial applicative structure can be embedded in an extensional topological model. We use the constructions from chapter 3 and 4.
The last and most extensive chapter deals with finite type structures within combinatorial algebras. The central theme here is finitetype extensionality, ie. extensionality on finite types. Wellknown models are tested against this property. It is shown that most of the literature examples are ftextensional regardless of their degree of global extensionality. To show that there is no connection between local and global extensionality, an extensional model is constructed that is not ftextensional.
Item Type:  Thesis (Doctoral) 

Report Nr:  HDS28 
Series Name:  ILLC Historical Dissertation (HDS) Series 
Year:  2018 
Additional Information:  Originally published: June 1988. 
Subjects:  Logic 
Depositing User:  Dr Marco Vervoort 
Date Deposited:  11 Jan 2022 23:21 
Last Modified:  11 Jan 2022 23:21 
URI:  https://eprints.illc.uva.nl/id/eprint/1860 
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