All Questions
6 questions
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Is possibile to define transfinite sum and product recursively? [closed]
On mathstackexchange a few days ago I published the following question where I asked about "transfinite" sum and products but actually nobody answered or gave an opinion with a comment: thus ...
11
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1
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400
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What is the Turing degree of the monadic theory of the real line?
The monadic theory of the real line is the set of all sentences in the monadic second-order language of order which are true in $\mathbb{R}$. In this 1982 paper, Gurevich and Shelah show that true ...
- 4,597
5
votes
0
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317
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$\Sigma_n$-complete sets in the Levy hierarchy
Recall that a set $A \subseteq \mathbb N$ is (many-one, Turing) $\Sigma_n$-complete if it's $\Sigma_n$ and any other $\Sigma_n$ set (many-one, Turing) reduces to it. This definition actually makes ...
- 1,882
19
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1
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747
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What non-standard model of arithmetic does Hofstadter reference in GEB?
Following some of the coolest bits of Hofstadter's Gödel, Escher, Bach, extensions of the standard model of arithmetic are described. A ways in, the paragraph "Supernatural Addition and Multiplication"...
- 1,288
18
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3
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Is Robinson Arithmetic biinterpretable with some theory in LST?
Let ZFC$^{\text{fin}}$ be ZFC minus the axiom of infinity plus the negation of the axiom of infinity. It is well-known that ZFC$^{\text{fin}}$ is biinterpretable with Peano Arithmetic. In this sense ...
- 3,267
7
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1
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198
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A well-behaved $A$ that is almost contained in every element of some filter for a countable arithmetically closed family $\mathfrak X$
The question has relevance for constructing Scott sets with certain extra desirable properties.
Suppose that $\mathfrak X$ is a countable arithmetically closed family of subsets of $\mathbb N$: ...
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