Stronger ideals over ${\cal P}_{\kappa }\lambda $

Volume 174 / 2002

Yo Matsubara Fundamenta Mathematicae 174 (2002), 229-238 MSC: Primary 03E55; Secondary 03E35. DOI: 10.4064/fm174-3-3


In §1 we define some properties of ideals by using games. These properties strengthen precipitousness. We call these stronger ideals. In §2 we show some limitations on the existence of such ideals over ${\cal P}_{\kappa}\lambda$. We also present a consistency result concerning the existence of such ideals over ${\cal P}_{\kappa}\lambda$. In §3 we show that such ideals satisfy stronger normality. We show a cardinal arithmetical consequence of the existence of strongly normal ideals. In § 4 we study some “large cardinal-like” consequences of stronger ideals.


  • Yo MatsubaraNagoya University
    Chikusa-ku, Nagoya, 464-8601, Japan

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