\(C(\infty,\infty)\):  The Axiom of Choice: Every  set  of  non-empty sets has a choice function.

If \({\cal L}\)  is  a  lattice  isomorphic  to the  lattice  of subalgebras of some unary universal algebra (a unary universal algebra is one with only unary or nullary operations) and \(\alpha \) is an automorphism of \({\cal L}\) of order 2 (that is, \(\alpha ^{2}\)  is  the  identity) then there is a unary algebra \(\frak A\)  and an isomorphism \(\rho \) from \({\cal L}\) onto the lattice of subalgebras of \(\frak A^{2}\) with \[\rho(\alpha(x))=(\rho(x))^{-1} (= \{(s,t) : (t,s)\in\rho(x)\})\] for all \(x\in  {\cal L}\).