  Turning now to the case in which L is an infinitary language  L(κ,λ), what  would be a suitable coding structure in this case? We remarked at the beginning that infinitary languages were suggested by the possibility of thinking of formulas as set-theoretical objects, so let us try to obtain our coding structure by thinking about what kind of set-theoretical objects we should take infinitary formulas to be. Given the fact that, for each φ∈Form(κ,λ), φ and its subformulas, subsubformulas, etc., are all of length &lt; κ,[6]  a moment's reflection reveals that formulas of  L(κ,λ) “correspond”  to sets x hereditarily of cardinality &lt; κ in the sense that x, its members, its members of members, etc., are all of cardinality &lt; κ. The collection of all such sets is written H(κ). H(ω) is the collection of hereditarily finite sets introduced above, and H(ω1) that of all hereditarily countable sets.