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Almost minimal varieties related to fuzzy logic

Katoh Y., Kowalski T., Ueda M.

Reports on Mathematical Logic

2006

Nr 41,spec. iss.

173-194

We present constructions producing continua of almost minimal subvarieties of certain varieties related to fuzzy logic. We also prove that there are only countably many almost minimal varieties of Hajek's BL-algebras --- all of them rather well known. Some contrasting results on varieties satisfying the 2-potency condition x3 = x2 are also included. The uncountabil- ity results have circulated rather widely in preprint (cf. [10]); this paper is meant to emphasise a general scheme that our construc- tions fall under.