The following statements are the main results of the paper: (a) cf(u) > ω and cf(uκ) > ω for every uncountable cardinal κ where uκ is the generalized ultrafilter number. (b) If κ > ℵ0 is regular and rκ < dκ then rκ = uκ, where rκ is the generalized reaping number and dκ is the generalized dominating number. (c) The relations rλ < dλ and uλ < dλ are consistent for a strong limit singular cardinal λ.
Bibliographical noteFunding Information:
manuscript and a lot of helpful suggestions. Both authors were supported by the ERC grant 338821. This is publication 1143 of the second author.
© Instytut Matematyczny PAN, 2020
- Pcf theory. Received 25 June 2018; revised 22 January 2019
- Reaping and dominating numbers
- Ultrafilter number