We consider the set of jumps below a Turing degree, given by JB={x':x≤a}, with a focus on the problem: Which recursively enumerable degrees a are uniquely determined by JB? Initially, this is motivated as a strategy to solve the rigidity problem for the partial order R of r.e. degrees. Namely, we show that if every high2 r.e. degree a is determined by JB, then R cannot have a nontrivial automorphism. We then defeat the strategy—at least in the form presented—by constructing (...) pairs a0, a1 of distinct r.e. degrees such that JB=JB within any possible jump class {x:x'=c}. We give some extensions of the construction and suggest ways to salvage the attack on rigidity. (shrink)

We study the weak truth table 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.

Migrant farm workers recruited under Canada’s temporary employment programs work in difficult environments, under poor working conditions, and live in unsafe housing in remote rural communities. Fearful of repatriation or replacement, many accept their working and living conditions as part of a necessary sacrifice to improve their living conditions and those of their families in the countries of origin. At the same time, some migrant farm workers assert their agency by escaping from farms, subverting regulations, or challenging various forms of (...) discipline used to control their bodies and activities. Following Isin and Nielsen (2008), we refer to these actions as “acts of citizenship.” Drawing on research conducted among migrant farm workers during the COVID-19 pandemic in the province of Quebec, Canada, we situate these acts, particularly the tendency to escape from abusive and exploitative working relationships, in a particular space and time shaped by the COVID-19 pandemic. More specifically, we demonstrate the link between these acts and certain conditions and opportunities that arose at that time, such as increased support for migrant farmworkers by a non-governmental organization and the facilitation of movement of migrant farmworkers across the Canada-U.S.-border by the “migration industry.”. (shrink)