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2007 Categories of Topological Spaces and Scattered Theories
R. W. Knight
Notre Dame J. Formal Logic 48(1): 53-77 (2007). DOI: 10.1305/ndjfl/1172787545

Abstract

We offer a topological treatment of scattered theories intended to help to explain the parallelism between, on the one hand, the theorems provable using Descriptive Set Theory by analysis of the space of countable models and, on the other, those provable by studying a tree of theories in a hierarchy of fragments of infinintary logic. We state some theorems which are, we hope, a step on the road to fully understanding counterexamples to Vaught's Conjecture. This framework is in the early stages of development, and one area for future exploration is the possibility of extending it to a setting in which the spaces of types of a theory are uncountable.

Citation

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R. W. Knight. "Categories of Topological Spaces and Scattered Theories." Notre Dame J. Formal Logic 48 (1) 53 - 77, 2007. https://doi.org/10.1305/ndjfl/1172787545

Information

Published: 2007
First available in Project Euclid: 1 March 2007

zbMATH: 1123.03020
MathSciNet: MR2289897
Digital Object Identifier: 10.1305/ndjfl/1172787545

Subjects:
Primary: 03C15, 06E15
Secondary: 18B30, 54B30

Rights: Copyright © 2007 University of Notre Dame

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Vol.48 • No. 1 • 2007
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