We isolate a new class of ultrafilters on N, called “quasi-selective” because they are intermediate between selective ultrafilters and P-points. (Under the Continuum Hypothesis these three classes are distinct.) The existence of quasi-selective ultrafilters is equivalent to the existence of “asymptotic numerosities” for all sets of tuples A ⊆ N^k. Such numerosities are hypernatural numbers that generalize finite cardinalities to countable point sets. Most notably, they maintain the structure of ordered semiring, and, in a precise sense, they allow for a natural extension of asymptotic density to all sets of tuples of natural numbers.
Autori interni: | |
Autori: | Blass A; Di Nasso M; Forti M |
Titolo: | Quasi-selective ultrafilters and asymptotic numerosities |
Anno del prodotto: | 2012 |
Digital Object Identifier (DOI): | 10.1016/j.aim.2012.06.021 |
Appare nelle tipologie: | 1.1 Articolo in rivista |