Abstrakt
We obtain an array of consistency results concerning trees and stationary reflection at double successors of regular cardinals kappa, updating some classical constructions in the process. This includes models of CSR(kappa(++)) boolean AND TP(kappa(++)) (both with and without AP(kappa(++))) and models of the conjunctions SR(kappa++) boolean AND wTP(kappa(++)) boolean AND AP(kappa(++)) andAP(kappa(++)) boolean AND SR(kappa(++)) (the latter was originally obtained in joint work by Krueger and the first author [9], and is here given using different methods).
Analogs of these results with the failure of SH(kappa(++)) are given as well. Finally, we obtain all of our results with an arbitrarily large 2 kappa, applying recent joint work by Honzik and the third author.