AbstractIn transfinite arithmetic 2nis defined as the cardinality of the family ofallsubsets of some setvwith cardinalityn.However, in the arithmetic of recursive equivalence types (RETs) 2Nis defined as the RET of the family ofall finitesubsets of some setvof nonnegative integers with RETN.Supposevis a nonempty set.Sis aclass over v, ifSconsists of finite subsets ofvand hasvas its union. Such a class is anintersecting class(IC) overv, if every two members ofShave a nonempty intersection. An IC overvis called amaximal IC(MIC), if it is not properly included in any IC overv.It is known and readily proved that every MIC over a finite setvof cardinalityn≥ 1 has cardinality 2n‐1. In order to generalize this result we introduce the notion of an ω‐MIC overv.This is an effective analogue ot the notion of an MIC overvsuch that a class over afinitesetvis an ω‐MIC iff it is an MIC. We then prove that every ω‐MIC over anisolatedsetvof RETN≥ 1 has RET 2N‐1. This is a generalization, for while there only are χ0finite sets, there are ϰ isolated sets, wherecdenotes the cardinality of the continuum, namely all the finite sets and thecimmun