Statement:
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 \(x\in {\cal L}\).
Howard_Rubin_Number: 268
Parameter(s): This form does not depend on parameters
This form's transferability is: Unknown
This form's negation transferability is: Negation Transferable
Article Citations:
Lampe-1974: Subalgebra lattices of unary algebras and an axiom of choice
Book references
Note connections: