Polish group actions and effectivity
Barbara Majcher-Iwanow
TL;DR
This paper generalizes Nadel's results on the connection between Scott sentences and admissible sets to broader orbit equivalence relations arising from Polish group actions on Polish spaces.
Contribution
It extends the relationship between Scott sentences and admissible sets to all orbit equivalence relations induced by Polish group actions.
Findings
Generalized Nadel's result to arbitrary Polish group actions
Established a link between Scott sentences and admissible sets in this broader context
Enhanced understanding of orbit equivalence relations in descriptive set theory
Abstract
We extend the result of Nadel describing the relationship between approximations of canonical Scott sentences and admissible sets to the general case of orbit equivalence relations induced on an arbitrary Polish space by a Polish group action.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Constraint Satisfaction and Optimization