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Let 2 = {0,1}. We show that the interval of partial clones containing the set of all selfdual monotonic partial functions is infinite on 2. We also study some partial clones in that interval.
Let 2 = {0,1} and let M be a monoid on 2. The monoidal interval determined by M is the set of all partial clones on 2 whose foundation is M. We study monoidal intervals determined by several monoids on 2. Among other things, we show that if M is a monoid of total functions and contains a non-trivial unary function on 2, then the monoidal interval determined by M consists of total clones on 2. Moreover,...
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