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.
|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|
|Keywords:||Computable structure theory, Continuous logic|
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