Low sets without subsets of higher many-one degree

摘要

Given a reducibility ≤r , we say that an infinite set A is r-introimmune if A is not r-reducible to any of its subsets B with |AB| = ∞. We consider the many-one reducibility ≤m and we prove the existence of a low_1 m-introimmune set in Π_1~0 and the existence of a low1 bi-m-introimmune set.