Some properties of maximal sets
Roland Sh. Omanadze, Irakli O. Chitaia · Logic Journal of IGPL · 2015
Let M1 and M2 be maximal sets, M10, M11 and M20, M21 be non-trivial splittings of M1 and M2, respectively. In this article we prove that if M10≡1M20, then M11≡1M21, M1≡mM2 and [M1≤1M2 or M2≤1M1]. It follows that if M10≡Q1M20, then M10≡1M20 and M1≡mM2. Also, we show that if A, B are major subsets of M1 and M2, respectively, and M1∖A≡Q1M2∖B, then M1∖A≡mM2∖B, A≡mB and M1≡mM2.