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The Scott set problem.

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$\mathfrak X$ such that

$(\omega, {\mathfrak X})\models WKL_0$ , Assume

$\lnot{\sf CH}$ . Is every Scott set the standard system of...")

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A Scott set is a set of sets of natural numbers $\mathfrak X$ such that $(\omega, {\mathfrak X})\models WKL_0$ , Assume $\lnot{\sf CH}$ . Is every Scott set the standard system of a nonstandard model of \PA?

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