The theory of hereditarily bounded sets
Emil Jeřábek · Mathematical logic quarterly · 2022
Abstract We show that for any , the structure of sets that are hereditarily of size at most k is decidable. We provide a transparent complete axiomatization of its theory, a quantifier elimination result, and tight bounds on its computational complexity. This stands in stark contrast to the structure of hereditarily finite sets, which is well known to be bi‐interpretable with the standard model of arithmetic .