Let
be an infinite set of urelements, and let be an enlargement of
the superstructure . Let be finitary algebras with finitely many operations,
and let and be their extension monads
in .
Let
be a homomorphism. Then is internally extendable provided that there is an internal
subalgebra of which contains and there is a homomorphism
such that if , then .
For a homomorphism , the following are equivalent:
1.
is internally extendable and is a subalgebra of ,
2. For some homomorphism , is the restriction to of .
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