Complete and incomplete Boolean degrees
Sergey Seraphimovich Marchenkov · Problems of Information Transmission · 2010
We study the partially ordered set of Boolean P 2-degrees. We introduce the notions of complete and incomplete Boolean degrees. We show that for each complete P 2-degree there exist both a countable decreasing chain of P 2-degrees and a countable antichain of P 2-degrees. We prove that above each incomplete P 2-degree there is a continuum of P 2-degrees. Thus, in total we show that in the partially ordered set of P 2-degrees there are no maximal elements.