Abstract:Several equivalent conditions for filters are given, and the definition of obstinate filters is introduced. Obstinate filters, maximal implicative filters and maximal positive implicative filters are proved equivalent to each other. It is also concluded that ultrafilters are obstinate filters and obstinate filters are prime filters. An equivalent condition for the obstinate filterLis provided through implication homomorphism, that is, for arbitrary lattice implication algebraL′,there always exists an implication homomorphism fromLtoL′,such that this filter is a dual kernel of this homomorphism.