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Ultraproducts and Higher Order Models

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thesis
posted on 08.11.2021, 20:15 authored by Malcolm, Wilfred Gordon

The programme of work for this thesis began with the somewhat genenal intention of parallelling in the context of higher order models the ultraproduct construction and its consequences as developed in the literature for first order models. Something of this was, of course, already available in the ultrapower construction of W.A.J. Luxemburg used in Non Standand Analysis. It may have been considered that such a genenal intention was not likely to yield anything of significance oven and above what was already available from viewing the higher order situation as a 'many sorted' first order one and interpreting the first order theory accordingly. In the event, however, I believe this has proved not to be so. In particular the substructure concepts developed in Chapter II of this thesis together with the various embedding theorems and their applications are not immediately available fnom the first order theory and seem to be of sufficient worth to warrant developing the higher order theory in its own terms. This, anyway, is the basic justification for the approach and content of the thesis.

History

Copyright Date

01/01/1972

Date of Award

01/01/1972

Publisher

Te Herenga Waka—Victoria University of Wellington

Rights License

Author Retains Copyright

Degree Discipline

Mathematics & Logic

Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level

Doctoral

Degree Name

Doctor of Philosophy

Victoria University of Wellington Item Type

Awarded Doctoral Thesis

Language

en_NZ

Victoria University of Wellington School

School of Mathematics, Statistics and Computer Science

Advisors

Hughes, G E; Seelye, C J; Cresswell, M J