Dissertation/Thesis Abstract

Computable Continuous Structure Theory
by Moody, James Gardner, Ph.D., University of California, Berkeley, 2019, 116; 13881481
Abstract (Summary)

We investigate structures of size at most continuum using various techniques originating from computable structure theory and continuous logic. Our approach, which we are naming "computable continuous structure theory", allows the fine-grained tools of computable structure theory to be generalized to apply to a wide class of separable completely-metrizable structures, such as Hilbert spaces, the p-adic integers, and many others. We can generalize many ideas, such as effective Scott families and effective type-omitting, to this wider class of structures. Since our logic respects the underlying topology of the space under consideration, it is in some sense more natural for structures with a metrizable topology which is not discrete.

Indexing (document details)
Advisor: Slaman, Theodore, Montalbán, Antonio
Commitee: Steel, John, Scanlon, Thomas, Holliday, Wesley, Christ, Michael
School: University of California, Berkeley
Department: Logic & the Methodology of Science
School Location: United States -- California
Source: DAI-A 81/3(E), Dissertation Abstracts International
Subjects: Logic, Mathematics
Keywords: Computable structure theory, Continuous logic
Publication Number: 13881481
ISBN: 9781085783897
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