Valued fields with finitely many defect extensions of prime degree

We prove that a valued field of positive characteristic [Formula: see text] has only finitely many distinct Artin–Schreier extensions (which is property infinite NTP 2 fields) dense in its perfect hull. As consequence, it deeply ramified and text]-divisible value group residue field. Further, we partial analogue for fields mixed observe an open problem about 1-units this setting. Finally, fill gap occurred proof earlier paper which first introduced classification defect extensions.