# Invariant sets in topology and logic

```@article{Vaught1974InvariantSI,
title={Invariant sets in topology and logic},
author={Robert L. Vaught},
journal={Fundamenta Mathematicae},
year={1974},
volume={82},
pages={269-294}
}```
• R. Vaught
• Published 1974
• Mathematics
• Fundamenta Mathematicae
109 Citations
Careful choices - a last word on Borel selectors
• J. Burgess
• Mathematics
Notre Dame J. Formal Log.
• 1981
Selector theory as surveyed in [13] and [14] deals with the following problem (instances of which arise in control theory, probability, mathematical economics, operator theory, etc.): We are given a
The effective Borel hierarchy
Let K be a subclass of Mod(L) which is closed under isomorphism. Vaught showed that K is Σα (respectively, Πα) in the Borel hierarchy iff K is axiomatized by an infinitary Σα (respectively, Πα)
Selectors for Borel sets with large sections
We prove a result asserting the existence of a Borel selector for a Borel set in the product of two Polish spaces. This subsumes a number of results about Borel selectors for Borel sets having large
An Application of Invariant Sets to Global Definability
Vaught's "*-transform method" is applied to derive a global definability theorem of M. Makkai from a classical theorem of Lusin on countable-to-one continuous functions.
A Selector for Equivalence Relations with G δ Orbits
Assume A" is a Polish space and E is an open equivalence on X such that every equivalence class is a Gs set. We show that there is a Gs transversal for E. It follows that for any separable C*-algebra
A selector for equivalence relations with _{} orbits
Assume X is a Polish space and E is an open equivalence on X such that every equivalence class is a G6 set. We show that there is a G6 transversal for E. It follows that for any separable C*-algebra
On the measurability of orbits in Borel actions
We replace measure with category in an argument of G. W. Mackey to characterize closed subgroups H of a totally nonmeager, 2nd countable topological group G in terms of the quotient Borel structure
The conjugacy problem for automorphism groups of countable homogeneous structures
• Mathematics
Math. Log. Q.
• 2016
In each case, the precise complexity of the conjugacy relation in the sense of Borel reducibility of automorphism groups of a number of countable homogeneous structures is found.
A L\'opez-Escobar theorem for metric structures, and the topological Vaught conjecture
• Mathematics
• 2014
We show that a version of L\'opez-Escobar's theorem holds in the setting of logic for metric structures. More precisely, let \$\mathbb{U}\$ denote the Urysohn sphere and let
Notions of Relative Ubiquity for Invariant Sets of Relational Structures
• Mathematics
J. Symb. Log.
• 1990
This work considers the collection of all L-structures on the set of natural numbers ω as a space as a compact metric space, and gives a notion of relative ubiquity, or largeness, for invariant sets of structures on ω.