# Tagged Questions

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### What's the difference between a logic, an internal logic (language) of a category, an internal logic of a topos and a type theory?

maybe this question doesn't make sense at all. I don't know exactly the meaning of all these concepts, except the internal language of a topos (and searching on the literature is not helping at all). ...
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### The deep structure of logical formulas

A long-standing question to which I never found a concise answer is: Is there something like an unambiguous deep structure of a formula of propositional logic, opposed to its comparingly ...
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### Sigma hierarchy of logical formulae

In some papers on mathematical logic I've found references to hierarchy like $\Sigma_1^0$-sentence and so on. What does it mean? What is $\Sigma_n^m$, what is $n$ and $m$ here?
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### How does one generally use partial function in logical statements?

How does one generally use partial function in logical statements? How it's done in practice? Specifically, let $M$ by a Turing machine, $f_M:\{0,1\}^*\to\{0,1\}$ the characteristic function which ...
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### Help with formulating a mathematical logic formula

I need to write a precise mathematical expression to formulate an algorithm that could be implemented in software. It has the following simple logic: An Internet user of the software in a ...
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### What underlies formal logic (or math, generally)?

I read a useful definition of the word understanding. I can't recall it verbatim, but the notion was that understanding is 'data compression': understanding happens when we learn one thing that ...
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### Function problem vs. decision problem

Take the set $FP$ of number-theoretic functions that are computable in polynomial time. Let us restrict to those functions with range in $\{0,1\}$, $FP_{0,1}$. Is there any correspondence with ...