Density-like and generalized density ideals

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Journal of Symbolic Logic 87 (1):228-251 (2022)
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Abstract

We show that there exist uncountably many pairwise nonisomorphic density-like ideals on $\omega $ which are not generalized density ideals. In addition, they are nonpathological. This answers a question posed by Borodulin-Nadzieja et al. in [this Journal, vol. 80, pp. 1268–1289]. Lastly, we provide sufficient conditions for a density-like ideal to be necessarily a generalized density ideal.

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10.1017/jsl.2021.95

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References found in this work

Analytic ideals and their applications.Sławomir Solecki - 1999 - Annals of Pure and Applied Logic 99 (1-3):51-72.
Analytic ideals and cofinal types.Alain Louveau & Boban Velickovi - 1999 - Annals of Pure and Applied Logic 99 (1-3):171-195.
Continuum-many Boolean algebras of the form.Michael Oliver - 2004 - Journal of Symbolic Logic 69 (3):799-816.

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