The rudin-keisler ordering of p-points under

M. E. Rudin (1971) proved, under CH, that for each P-point p there exists a P-point q strictly RK-greater than p. This result was proved under by A. Blass (1973), who also showed that each RK-increasing-sequence of P-points is upper bounded by a P-point, and that there is an order embedding of the real line into the class of P-points with respect to the RK-ordering. In this paper, the results cited above are proved under the (weaker) assumption that. A. Blass asked in 1973 which ordinals can be embedded in the set of P-points, and pointed out that such an ordinal cannot be greater than. In this paper it is proved, under, that for each ordinal <![CDATA[ \alpha, there is an order embedding of into P-points. It is also proved, under, that there is an embedding of the long line into P-points.