# Tagged Questions

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### What are $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$?

Sometimes reading on wikipedia or in this site (and in very different context like topology, arithmetic and logic) I have found these symbols $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$. They are ...
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### What would be arithmetic hierarchy of $\Sigma_1^0 \wedge \Pi_1^0$?

What would be arithmetic hierarchy of the form of formula like $\phi \wedge \psi$ where $\phi$ is $\Sigma_1^0$ and $\psi$ is $\Pi_1^0$? Prenex normal form seems to give me no answer for this.
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### Formula of hierarchies - arithmetic hierarchy and analytical hierarchy

I am recently learning on these topics, and to help understand these things, it would be helpful if some examples of formula of various arithmetic hierarchies and analytical hierarchies are provided. ...
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### Members of (lightface) Borel sets

I'm fairly certain this question has a very simple answer, and that I've learned it before; I just can't seem to remember it. Suppose I have a nonempty lightface Borel set $X\subseteq 2^\omega$. What ...
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### Which are “big theorems” of descriptive set theory?

Question: If one were to fully understand 10 theorems in DST, or 15,20,25,30 theorems, which ones would be the most important to understand in order to work towards an understanding of descriptive set ...
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### From lightface $\Sigma^1_1$ to boldface $\mathbf\Delta^1_1$

Fix some standard Polish space, e.g. Baire's space. It's a simple observation that every $\Delta^1_1$ is also $\mathbf\Delta^1_1$. It is the same observation that $\Sigma^1_1$ becomes ...
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### An application of Descriptive set theory in Model theory.

In page 162 of D.Marker Model theory book he proved that the set $S_n(F,T)$ of all $F$-types realized by some $n$-tuple in some countable model of $T$ is analytic (this is with any $F$:= $countable$ ...
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### Question about a defined function in D.Marker Model Theory book.

In page 162 of D.Marker Model theory book he proved that the set $S_n(F,T)$ of all $F$-types realized by some $n$-tuple in some countable model of $T$ is analytic (this is with any $F$:= $countable$ ...
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### How does Borelness overlap with definability, computability, or constructiveness?

Background: I am writing a short paper aimed at math undergrads and focused as narrowly as possible on Borel equivalence relations. So, e.g., I am not assuming familiarity with recursion theory and am ...