Corrigendum to “Sets with no subsets of higher weak truth-table degree”, Reports on Mathematical Logic, 53 (2018), 3–17
Patrizio Cintioli · Reports on Mathematical Logic · 2020
In the paper we prove the existence of an arithmetical set without subsets of higher weak truth-table degree.Mistakenly, we believed that there were no known reducibilities strictly contained in the Turing reducibility (on all 2 ω ) incomparable with ≤ wtt and having the corresponding degree notion.Actually in [1] such a reducibility has been introduced (D + -reducibility).Furthermore, we have not sufficiently highlighted our plan to consider only reducibilities having the corresponding degree notion.Therefore, the sentence in the last three lines of the introduction in the paper is not correct.Namely, the sentence "Since we currently do not know intermediate reducibilities between ≤ wtt and ≤ T , we deduce that for all the known reducibilities ≤ r strictly contained in ≤ T there are arithmetical r-introimmune sets."