The superrosy field conjecture via PRC fields

A field is PRC (pseudo real closed) if it satisfies the PRC property; its absolute Galois group is small if it has only finitely many closed subgroups of each finite index. The superrosy field conjecture via PRC fields. Every infinite superrosy field is perfect PRC with small absolute Galois group. Perfect PAC fields with small absolute Galois group and orderable PRC fields with small absolute Galois group are known to be superrosy, so the source presents this as the strongest possible extension of the preceding conjecture; it remains unresolved in the supplied text.