Instead of considering just one relation, we could consider the structure formed by a finite set of relations R1,…, Rk, of arities m1,…,mk, respectively, all on the same universe E; such a structure is called a multirelation; the sequence of arities m1,…,mk is called the signature (or similarity type) of the multirelation. Given a second multirclation (S1,…, Sk) with universe F and the same signature, an isomorphism from (R1,…, Rk) to (S1,…, Sk) is a function s from E to F that is an isomorphism from R1 to S1,…, from Rk to Sk. The notions of extension, embedding, local isomorphism, p-isomorphism, etc. are defined the same way as for relations. For the language associated with a multirelation, or more precisely with its signature, we now must introduce k relation symbols, instead of just one: one of arity m1 to denote R1, …, one of arity mk to denote Rk.
Function Symbol Atomic Formula Relation Symbol Constant Symbol Bibliographic Note
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