Applicazioni della teoria descrittiva degli insiemi a problemi di classificazione per classi di strutture e relazioni d’equivalenza
Universal analytic preorders arising from surjective functions
Examples are presented of Σ₁¹-universal preorders arising by requiring the existence of particular surjective functions. These are: the relation of epimorphism between countable graphs; the relation of being a continuous image (or a continuous image of some specific kind) for continua; the relation of being continuous open image for dendrites.
Complete sequences of coanalytic sets
The notion of a complete sequence of pairwise disjoint coanalytic sets is investigated. Several examples are given and such sequences are characterised under analytic determinacy. The ideas are based on earlier results of Saint Raymond, and generalise them.
Conjugacy equivalence relation on subgroups
If G is a countable group containing a copy of F₂ then the conjugacy equivalence relation on subgroups of G attains the maximal possible complexity.
Page 1