Pequeñas particiones infinitas y otras características del ideal no centrado en ninguna parte

Por • 26 abr, 2022 • Sección: Opinion

Mario Jardón Santos

The textit{nowhere dense ideal} NC is introduced. It is a coanalytic ideal of ω×ω whose defining characteristic is that the sets of the form X×Y, where X,Y are infinite subsets of ω, are dense in the quotient $mathcal{P}(omegatimesomega)slashmathcal{NC}$. This quotient has countable partitions and consistently has partitions of size ω1 while a>ω1. This represents a huge contrast with other definable quotients. Other combinatorial features of this ideal are presented, as well as some results on a family of similar, higher dimensional ideals.

arXiv:2203.00234v1 [math.LO]

Logic (math.LO)

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