2018/01/19 by Switzer, Corey · 1 citation
#03E65 #0E35 #28A05 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1801.06497
Following a line of research initiated in \citeBBNN, I describe a general framework for turning reduction concepts of relative computability into diagrams forming an analogy with the Cichoń diagram for cardinal characteristics of the continuum. I show that working from relatively modest assumptions about a notion of reduction, one can construct a robust version of such a diagram. As an application, I define and investigate the Cichoń Diagram for degrees of constructibility relative to a fixed inner model W. Many analogies hold with the classical theory as well as some surprising differences. Along the way I introduce a new axiom stating, roughly, that the constructibility diagram is as complex as possible.