Form equivalence class Howard-Rubin Number: 88
Statement:
If \(m\) is a cardinal number and \({\cal L}\) 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 \(\frak A\) with \(|\hbox{domain }\frak A| \ge m\) 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: 88 C
Citations (articles):
Lampe [1974]
Subalgebra lattices of unary algebras and an axiom of choice
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References (books):
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