Generalized Descriptive Set Theory and Classification Theory
Jun 2014 · American Mathematical Soc.
Ebook
80
Pages
About this ebook
Descriptive set theory is mainly concerned with studying subsets of the
space of all countable binary sequences. In this paper the authors
study the generalization where countable is replaced by uncountable.
They explore properties of generalized Baire and Cantor spaces,
equivalence relations and their Borel reducibility. The study shows
that the descriptive set theory looks very different in this
generalized setting compared to the classical, countable case. They
also draw the connection between the stability theoretic complexity of
first-order theories and the descriptive set theoretic complexity of
their isomorphism relations. The authors' results suggest that Borel
reducibility on uncountable structures is a model theoretically natural
way to compare the complexity of isomorphism relations.
space of all countable binary sequences. In this paper the authors
study the generalization where countable is replaced by uncountable.
They explore properties of generalized Baire and Cantor spaces,
equivalence relations and their Borel reducibility. The study shows
that the descriptive set theory looks very different in this
generalized setting compared to the classical, countable case. They
also draw the connection between the stability theoretic complexity of
first-order theories and the descriptive set theoretic complexity of
their isomorphism relations. The authors' results suggest that Borel
reducibility on uncountable structures is a model theoretically natural
way to compare the complexity of isomorphism relations.
Descriptive set theory is mainly concerned with studying subsets of the
space of all countable binary sequences. In this paper the authors
study the generalization where countable is replaced by uncountable.
They explore properties of generalized Baire and Cantor spaces,
equivalence relations ...
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