It is proved that there exists a formula of first-order logic with only one non-logical symbol, a binary function symbol Ap signifying application, which uniformly defines inclusion in all BF(E)-models Some definabili...It is proved that there exists a formula of first-order logic with only one non-logical symbol, a binary function symbol Ap signifying application, which uniformly defines inclusion in all BF(E)-models Some definability results give an isomorphism between the group of bi-stable Ap -automorphisms of A and the group of permutations of A; it also implies that each BF(E)-model is determined, up to isomorphism, by the cardinal of its set of atoms.展开更多
基金Project partially supported by a post-doctor grant of the Chinese Academy of Sciences.
文摘It is proved that there exists a formula of first-order logic with only one non-logical symbol, a binary function symbol Ap signifying application, which uniformly defines inclusion in all BF(E)-models Some definability results give an isomorphism between the group of bi-stable Ap -automorphisms of A and the group of permutations of A; it also implies that each BF(E)-model is determined, up to isomorphism, by the cardinal of its set of atoms.
