On relative coimmunity
Thomas G. McLaughlin · Pacific Journal of Mathematics · 1965
Σ are sets of numbers such that A £ Σ and Σ -A is immune, we say that Δ is coimmune in Σ.(In case A -Wj, Σ -W k , for some j and k, we say instead that Δ is simple in Σ.) Similarly, if Δ ξΞ= Σ and Σ -A is hyperhyperimmune, we say that A is cohyperhyperimmune in 2 1 , or that A is hyperhy per simple in Σ 9 in case both z/ and Σ are r.e.(For definition and discussion of the notion of hyperhyperimmunity, the reader may consult [9] or [10]; the existence of hyperhypersimple sets is known from [5].) LEMMA 1.There exists a set of numbers, a, such that both a and its complement, a, are hyperhyperimmune.