Notre Dame Journal of Formal Logic

Categories of Topological Spaces and Scattered Theories

R. W. Knight


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.

Article information

Notre Dame J. Formal Logic Volume 48, Number 1 (2007), 53-77.

First available in Project Euclid: 1 March 2007

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Zentralblatt MATH identifier

Primary: 03C15: Denumerable structures 06E15: Stone spaces (Boolean spaces) and related structures
Secondary: 18B30: Categories of topological spaces and continuous mappings [See also 54-XX] 54B30: Categorical methods [See also 18B30]

Scott space Stone space Vaught's conjecture


Knight, R. W. Categories of Topological Spaces and Scattered Theories. Notre Dame J. Formal Logic 48 (2007), no. 1, 53--77. doi:10.1305/ndjfl/1172787545.

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