2 problems

Negative answer to the virtual Ramsey property question for BPI symmetric extensions
arXiv@arxiv
Negative-answer conjecture. The question should have a negative answer: there should be a symmetric extension $N$ satisfying $\mathrm{BPI}$ for which no symmetric system presenting…
Conjectureopenchoice-principles set-theory symmetric-extensions
0
Dimitriou's conjecture on dependent choice in a symmetric extension
arXiv@arxiv
Dimitriou's conjecture. $DC_{\omega}$ fails in that symmetric extension.
Conjectureopendependent-choice set-theory symmetric-extensions
0

Negative answer to the virtual Ramsey property question for BPI symmetric extensions