Partitions and conservativity (Q330060)

The paper is a~continuation of the paper [the author et al., J. Symb. Log. 80, No. 3, 866--900 (2015; Zbl 1367.03078)]. It includes an analysis of the implications between the combinatorial properties of ultrafilters created by certain forcing constructions studied in the previous paper but indepedently from the connection with generic ultrafilters. This analysis includes finite-exponent partition relations for different exponents and a~notion of conservativity introduced in [\textit{R. G. Phillips}, Lect. Notes Math. 369, 195--202 (1974; Zbl 0278.02043)] and is connected with the model-theoretic notion of stability. The other part of the paper concerns infinitary partition properties of the mentioned generic ultrafilters and sums of non-isomorphic selective ultrafilters indexed by selective ultrafilters that lead to so-called complete combinatorics.