Fuzzy logic with countable evaluated syntax revisited

In this paper, we revisit fuzzy logic with evaluated syntax EvŁ. An objection towards it is necessity to introduce logical constants (names of truth values) for all a∈[0,1] into its language which makes it uncountable. Hájek has shown in his book “Metamathematics of fuzzy logic” that when seeing EvŁ as RPL logic where the provability degree is an additional concept then we may confine only to rational logical constants. In this paper, we show that the same result can be obtained directly in EvŁ. The essential idea is to generalize slightly the concept of a complete fuzzy theory using the technique of EvŁ.