We study the weak truth table (wtt) degree spectra of first-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 finite- and infinite-signature structures. We show that, as a method of defining classes of reals, the wtt degree spectrum is, except for some trivial cases, strictly more expressive than the Turing degree spectrum.
"Weak Truth Table Degrees of Structures." Notre Dame J. Formal Logic 56 (2) 263 - 285, 2015. https://doi.org/10.1215/00294527-2864298