| Summary: | This paper is about ``imbrication algebras'', universal algebras with one binary operator in their signature, the operator for formation of ordered pairs, called here ``pairing operator'', and with the ``characteristic property of ordered pairs'' as their sole axiom. These algebras have been earlier introduced by the first author as reducts of ``aggregate algebras'', universal algebras proposed as models for a set theory convenient for formalization of data structures. The term ``aggregate'' is used to generalize three fundamental notions of set theory: set, atom and ordered pair. Thus, this paper initiates the research of aggregate algebras by narrowing the focus to one type of their main reducts -- the reduct which deals with ordered pairs.
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