Über zwei Bezeichnungssysteme für Ordinalzahlen.
We define an ultra -ideal of a lattice implication algebra and give equivalent conditions for an -ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra -ideal.
A mistake concerning the ultra -ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an -ideal to be an ultra -ideal are given. Moreover, the notion of an -ideal is extended to -algebras, the notions of a (prime, ultra, obstinate, Boolean) -ideal and an -ideal of an -algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in -algebra: (1) prime proper -ideal and Boolean -ideal,...
We characterize for which ultrafilters on is the ultrafilter extension of the asymptotic density on natural numbers -additive on the quotient boolean algebra or satisfies similar additive condition on . These notions were defined in [Blass A., Frankiewicz R., Plebanek G., Ryll-Nardzewski C., A Note on extensions of asymptotic density, Proc. Amer. Math. Soc. 129 (2001), no. 11, 3313–3320] under the name (null) and (*). We also present a characterization of a - and semiselective ultrafilters...