Maximal Tukey types, P-ideals and the weak Rudin-Keisler order

In this paper, we study some new examples of ideals on. with maximal Tukey type (that is, maximal among partial orders of size continuum). This discussion segues into an examination of a refinement of the Tukey order-known as the weak RudinKeisler order-and its structurewhen restricted to these ideals ofmaximal Tukey type. Mirroring a result of Fremlin (Note Mat 11:177-214, 1991) on the Tukey order, we also show that there is an analytic P-ideal above all other analytic P-ideals in the weak Rudin-Keisler order.

Automated summary

In this paper, we study new examples of ideals with maximal Tukey type and examine the structure of the weak Rudin-Keisler order when restricted to these ideals of maximal Tukey type. We also show the existence of an analytic P-ideal above all other analytic P-ideals in the weak Rudin-Keisler order, mirroring a result on the Tukey order by Fremlin.