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Noah Schweber
Noah Schweber
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David Roberts ♦
David Roberts ♦
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The monadic theory of the real linemonadic theory of the real line is the set of all sentences in the monadic second-order languagemonadic second-order language of order which are true in $\mathbb{R}$. In this 1982 paper, Gurevich and Shelah show that true first-order arithmetic is Turing-reducible to the monadic theory of the real line. (Shelah first showed it in the 1970's, but his original result assumed the continuum hypothesis.) But my question is, what is the Turing degree of the monadic theory of the real line?

Clearly the monadic theory of the real line is Turing reducible to true third-order arithmetic, but how does it compare to true second-order arithmetic, for instance?

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 first-order arithmetic is Turing-reducible to the monadic theory of the real line. (Shelah first showed it in the 1970's, but his original result assumed the continuum hypothesis.) But my question is, what is the Turing degree of the monadic theory of the real line?

Clearly the monadic theory of the real line is Turing reducible to true third-order arithmetic, but how does it compare to true second-order arithmetic, for instance?

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 first-order arithmetic is Turing-reducible to the monadic theory of the real line. (Shelah first showed it in the 1970's, but his original result assumed the continuum hypothesis.) But my question is, what is the Turing degree of the monadic theory of the real line?

Clearly the monadic theory of the real line is Turing reducible to true third-order arithmetic, but how does it compare to true second-order arithmetic, for instance?

Notice added Draw attention by Keshav Srinivasan
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Keshav Srinivasan
Keshav Srinivasan
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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 first-order arithmetic is Turing-reducible to the monadic theory of the real line. (Shelah first showed it in the 1970's, but his original result assumed the continuum hypothesis.) But my question is, what is the Turing degree of the monadic theory of the real line?

Clearly the monadic theory of the real line is Turing reducible to true third-order arithmetic, but how does it compare to true second-order arithmetic, for instance?