EN|RU Volume 20, No 2, 2013, P. 88-101 UDC 519.71 Marchenkov S. S. On maximal and minimal elements in partially ordered sets of Boolean degrees Abstract: The weakest variant of algorithmic reducibility called Boolean reducibility is considered. For various closed classes $Q$, the partially ordered sets $\mathcal L_Q$ of Boolean degrees are analyzed. It is proved that for many closed classes $Q$ the corresponding sets $\mathcal L_Q$ have no maximal elements. Examples of sufficiently large classes $Q$ are given for which the sets $\mathcal L_Q$ contain uncountably many maximal elements. It is established that for closed classes $T_{01}$ and $S$M the corresponding sets of degrees have uncountably many minimal elements. Bibliogr. 8. Keywords: Boolean reducibility, closed classes of Boolean functions. Marchenkov Sergey Serafimovich 1 1. Lomonosov Moscow State University, Leninskie gory, 119991 Moscow, Russia e-mail: ssmarchen@yandex.ru © Sobolev Institute of Mathematics, 2015