EQ-Algebras in progress

EQ-algebra is an algebra with three binary operations (meet, product, fuzzy equality) and a top element that has been introduced in [13] as an algebra of truth values for the fuzzy type theory (a higher-order fuzzy logic). Recall that till now, truth values in fuzzy type theory have been supposed to form either of IMTL, BL, MV or L Pi-algebra that are special residuated lattices. However, since fuzzy equality is a derived operation in residuated lattice, it is not so natural for fuzzy type theory as the EQ-algebra. In this paper, we continue the research of EQ-algebras. Namely, we have modified some axioms, show further properties of them and outline the filter theory.