Minimal numerations of positively computable families
It is proved that among computable numerations that are limit-equivalent to some positive numeration of a computable family of recursively enumerable sets, either there exists one least numeration, or there are countably many nonequivalent, minimal numerations. In particular, semilattices of computable numerations for computable families of finite sets and of weakly effectively discrete families of recursively enumerable sets either have a least element or possess countably many minimal elements.
KeywordsMathematical Logic Minimal Element Minimal Numeration Discrete Family Positive Numeration
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