Diamond principles and Tukey-top ultrafilters on a countable set

We provide two types of guessing principles for ultrafilter (^-_ (U), \ ᵖ_ (U) ) on which form subclasses of Tukey-top ultrafilters, and construct such ultrafilters in ZFC. These constructions are essentially different from Isbell's construction Isbell65 of Tukey-top ultrafilters. We prove using the Borel-Cantelli Lemma that full guessing is not possible and rule out several stronger guessing principles e. g. we prove that no Dodd-sound ultrafilters exist on. We then apply these guessing principles to force a q-point which is Tukey-top (answering a question from Benhanou/Dobrinen23), and prove that the class of ultrafilters which satisfy ^-_ is closed under Fubini sum. Finally, we show that ^-_ and ᵖ_ can be separated.