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Results tagged with descriptive-set-theory
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user 26705
Descriptive Set Theory is the study of definable subsets of Polish spaces, where definable is taken to mean from the Borel or projective hierarchies. Other topics include infinite games and determinacy, definable equivalence relations and Borel reductions between them, Polish groups, and effective descriptive set theory.
4
votes
Accepted
Perfectly transversable theories
The property you are asking for is a very strong condition on $T$. Let met try to rephrase the question more carefully:
The set of countable $\Sigma$-structures with universe $\omega$ is naturally a …
- 2,146
4
votes
0
answers
144
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Constructing Complicated Borel Subgroups of Polish Groups
Farah and Solecki showed the following in Borel subgroups of Polish groups:
Theorem: Every Polish group $G$ admits Borel subgroups of arbitrarily high Borel rank.
However, the construction is far from …
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4
votes
Is there a class of mathematical structures with non-isomorphic natural representations as a...
Perhaps I am misunderstanding the question, but here is what seems to be a counterexample (Lemma 9.2.2 from Su Gao Invariant Descriptive Set Theory):
Let $H$ be the class of countable well-orders. Th …
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9
votes
Accepted
Which reals are "hyperarithmetic modulo ordinals"?
In fact $\Delta^{1, ord}_1 = \mathbb{L} \cap \mathbb{R}$.
For suppose $(\phi(x, \overline{y})$, $\psi(x, \overline{y})$, $\overline{\alpha})$ is as you describe, defining $r \subset \omega$. We show …
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16
votes
Accepted
Can an ultrapower be undone by forcing?
For set-forcing, the answer is no, see the following article
Joel David Hamkins, Greg Kirmayer, and Norman Lewis Perlmutter, Generalizations of the Kunen inconsistency, Ann. Pure Appl. Logic 163 (201 …
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