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- W2517718905 abstract "Abstract Schweber [10] defined a reducibility that allows us to compare the computing power of structures of arbitrary cardinality. Here we focus on the ordered field ${cal R}$ of real numbers and a structure ${cal W}$ that just codes the subsets of ω . In [10], it was observed that ${cal W}$ is reducible to ${cal R}$ . We prove that ${cal R}$ is not reducible to ${cal W}$ . As part of the proof, we show that for a countable recursively saturated real closed field ${cal P}$ with residue field k , some copy of ${cal P}$ does not compute a copy of k ." @default.
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- W2517718905 date "2016-08-12" @default.
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- W2517718905 title "COMPARING TWO VERSIONS OF THE REALS" @default.
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- W2517718905 doi "https://doi.org/10.1017/jsl.2015.77" @default.
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