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Results tagged with descriptive-set-theory
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user 6942
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
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Question of combinatorics in the lower part of the Borel hierarchy.
Consider the case $2^\omega$ (the case of Baire space I believe is only notationally more complicated.) Let $(s_i : i<\omega)$ recursively enumerate $2^{<\omega}$ with $s_0=\varnothing$ and $s_i \sub …
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23
votes
Accepted
Why does inner model theory need so much descriptive set theory (and vice versa)?
I think that in some ways you have answered your question yourself: we see that to prove properties about sets, say within the projective hierarchy, we need representations of those sets of reals as t …
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10
votes
Accepted
Concerning Silver's result
Re Q1: Sy Friedman has shown by class forcing over L that there can be consistently a real r
with the r-admissibles precisely the recursively inaccessibles. (S Friedman, "Strong Coding" APAL, vol 35, …
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8
votes
Accepted
Higher recursion theory and reverse mathematics: What is to $\Pi^1_1$-$CA_0$ as $RCA_0$ is t...
I am getting the feeling there is some slight miss-match of terminology, or perhaps application of terminology is a better way of putting it? It is true that the (lightface) $\Pi^1_1$-$CA_0$ sets of i …
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10
votes
Large Cardinal Principles that Imply $\Sigma_3^1$-Generic Absoluteness
A proper class of measurables more than suffices.
It suffices for the generic absoluteness to have X-sharp exists for every set of ordinals X. Then the Martin-Solovay tree can be constructed through …
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