A type of collection and the collection of all and only those Collections some of whose instances (or instances of instances, or instances of instances of instances, etc.) are of different orders , where order is understood as follows. Let Individuals be zeroth-order things, collections of (only) Individuals first-order , ..., and collections of (only) Nth-order things (N+1)th-order . A more precise, recursive definition, then, is: a collection COL is an instance of variable-order Cyc collection if and only if COL has instances INST1 and INST2 such that either (i) INST1 and INST2 are of two different fixed orders N1 and N2, (ii) INST1 is of the fixed order N1 and INST2 is a varied-order collection, or (iii) INST1 and INST2 are both varied-order collections.

For example, abstract thing is a varied-order collection since it contains both (zeroth-order) abstract individuals and (higher-order) collections. Other instances of variable-order Cyc collection include intangible, type of thing, type of collection, and thing. Note that (by clauses ii and iii) any generalization of a varied-order collection is varied-order; and (by clause iii) any (non-empty) specialization of variable-order Cyc collection is varied-order.

Note that fixed-order Cyc collection (q.v.) and variable-order Cyc collection do _not_ constitute a partition of Collection: since the notion of order described above is not applicable to sets, set (e.g.) and its specializations are neither fixed-order nor varied-order collections.