[FOM] Fulfilment of semilatice & third level always has (isomorphic copy) of first level(?)

[Stanislav Barov]

Dear fomers?
May someone explain which sentences are equivalent to statament what
"All upper semilatices can be embeded in full semilatices" This 
construction is similar to dedecind's cuts fulfilment, but it is only the 
example.
I have second, more general question. Is thare a counterexample to
conjecture what any first level strusctures can be equivalently described
in terms of third levels statements, e.g. describable on third level.
For example set of maximal principial ideals in POS is (probably modulo) 
set of atoms.
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Stanislav Barov