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- W2883324280 abstract "Several researchers have recently established that for every Turing degree $boldsymbol{c}$, the real closed field of all $boldsymbol{c}$-computable real numbers has spectrum ${boldsymbol{d}~:~boldsymbol{d}'geqboldsymbol{c}}$. We investigate the spectra of real closed fields further, focusing first on subfields of the field $mathbb{R}_{boldsymbol{0}}$ of computable real numbers, then on archimedean real closed fields more generally, and finally on non-archimedean real closed fields. For each noncomputable, computably enumerable set $C$, we produce a real closed $C$-computable subfield of $mathbb{R}_{boldsymbol{0}}$ with no computable copy. Then we build an archimedean real closed field with no computable copy but with a computable enumeration of the Dedekind cuts it realizes, and a computably presentable nonarchimedean real closed field whose residue field has no computable presentation." @default.
- W2883324280 created "2018-08-03" @default.
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- W2883324280 date "2018-07-20" @default.
- W2883324280 modified "2023-09-30" @default.
- W2883324280 title "Degree spectra of real closed fields" @default.
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- W2883324280 doi "https://doi.org/10.1007/s00153-018-0638-z" @default.
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