类密度理想与广义密度理想
Density-Like and Generalized Density Ideals
摘要：
我们证明了在$ω$上存在不可数多个（高的和非高的）两两非同构的类密度理想，这些理想不是广义密度理想。此外，它们是非病理性的。这回答了Borodulin-Nadzieja，Farkas和Plebanek在[J. Symb. Log. \textbf{80}（2015），1268- 1289]。最后，我们给出了类密度理想必然是广义密度理想的充分条件。
英文摘要：
We show that there exist uncountably many (tall and nontall) pairwise nonisomorphic density-like ideals on $ω$ which are not generalized density ideals. In addition, they are nonpathological. This answers a question posed by Borodulin-Nadzieja, Farkas, and Plebanek in [J. Symb. Log. \textbf{80} (2015), 1268--1289]. Lastly, we provide sufficient conditions for a density-like ideal to be necessarily a generalized density ideal.
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