All Questions
5
questions
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Intersection of (relativized/preimage) measure 0 with every hyperarithmetic perfect set
Given a perfect tree $T$ on $2^{<\omega}$ viewed as a function from $2^{<\omega}$ to $2^{<\omega}$ define the measure of a subset of $[T]$ to be the measure of it's preimage under the usual ...
- 2,531
4
votes
1
answer
189
views
Borel ranks of Turing cones
For a non recursive $x \in 2^{\omega}$, define $C_x = \{y \in 2^{\omega}: x \leq_T y\}$. Note that $y \in C_x$ iff $(\exists e)(\forall n)(\Phi^y_e(n) = x(n))$ where $\Phi_e$ is the $e$th Turing ...
- 118
5
votes
0
answers
167
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What is known about these "explicitly represented" spaces?
Apologies if this is too low-level. A related question that I asked on the Math Stack Exchange got no answers after a year, so I thought it might be better to ask this one here.
The standard approach ...
- 3,398
2
votes
2
answers
125
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Finding 1-generic paths through a tree $T \subseteq 2^{<\omega}$
Consider Cantor space $2^\omega$ with the standard topology generated by open sets $[\sigma] = \{ \sigma^\frown x: x \in 2^\omega \}$. If $A \subseteq 2^{<\omega}$ and $x \in 2^\omega$, we say $A$ ...
2
votes
1
answer
179
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Detecting comprehension topologically
This question basically follows this earlier question of mine but shifting from standard systems of nonstandard models of $PA$ to $\omega$-models of $RCA_0$. For $X$ a Turing ideal we get the map $c_X$...
- 19k