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:||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|