Small infinite partitions and other features of the Nowhere Centered ideal

Author name not available (Why is that?)

Publication date: 1 March 2022

Abstract: The extit{nowhere dense ideal}

m a t h c a l N C

is introduced. It is a coanalytic ideal of

o m e g a i m e s o m e g a

whose defining characteristic is that the sets of the form

X i m e s Y

, where

X, Y

are infinite subsets of

o m e g a

, are dense in the quotient

m a t h c a l P (o m e g a i m e s o m e g a) s l a s h m a t h c a l N C

. This quotient has countable partitions and consistently has partitions of size

o m e g a_{1}

while

m a t h f r a k a > o m e g a_{1}

. 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.

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