Abstract
We study the weak truth table (wtt) degree spectra of rst-order relational structures. We prove a dichotomy among the possible wtt degree spectra along the lines of Knight’s upward-closure theorem for Turing degree spectra. We prove new results contrasting the wtt degree spectra of nite- and innite-signature structures. We show that, as a method of dening classes of reals, the wtt degree spectrum is, except for some trivial cases, strictly more expressive than the Turing degree spectrum.
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