HDS-37: Some extensional term models for combinatory logics and Lambda-Calculi

HDS-37: Barendregt, Henk (2023) Some extensional term models for combinatory logics and Lambda-Calculi. Doctoral thesis, Rijksuniversiteit Utrecht.

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This thesis is concerned with combinatorial logic, not as a basis for the rest of mathematics, but as a formal system for the study of computational procedures. Chapter I provides an overview and extension of already known material.
In Chapter II, the ω-rule is introduced and, using transfinite induction, it is proven that the extension of combinatorial logic with the ω-rule is consistent. Furthermore, the existence of universal generators is proven. For terms that are not universal generators, the ω rule is a derivative rule.
In Chapter III, a number of other consistency results are proven, yielding several non-elementary equivalent models of combinatorial logic.
Proofs of the above results usually use conservative extensions of combinatorial logic. A new proof technique plays an important role here, namely the underlining method. This method formalizes the concept of residue and thus avoids the otherwise rather cumbersome arguments.

Item Type: Thesis (Doctoral)
Report Nr: HDS-37
Series Name: ILLC Historical Dissertation (HDS) Series
Year: 2023
Additional Information: Originally published: June 1971.
Subjects: Logic
Depositing User: Dr Marco Vervoort
Date Deposited: 24 Oct 2023 13:34
Last Modified: 24 Oct 2023 13:42
URI: https://eprints.illc.uva.nl/id/eprint/2277

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