Diamond principles and Tukey-top ultrafilters on a countable set

We provide two types of guessing principles for ultrafilter (⁻λ(U), \ ᵖ_λ(U)) on ω 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 ω. 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 ⁻_λ is closed under Fubini sum. Finally, we show that ⁻_λ and ᵖ_λ can be separated.