Enlargement

In geometry, the term "enlargement" is a synonym for expansion.

In nonstandard analysis, let  be a set of urelements, and let  be the superstructure with individuals in :

1. ,

2. ,

3. .

Let  be a superstructure monomorphism, with  and  for . Then  is an enlargement of  provided that for each set  in , there is a hyperfinite set  that contains all the standard entities of .

It is the case that  is an enlargement of  if and only if every concurrent binary relation  satisfies the following: There is an element  of the range of  such that for every  in the domain of , the pair  is in the relation .

REFERENCES

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Schmid, J. "Completing Boolean Algebras by Nonstandard Methods." Zeitschr. für Math. Logik u. Grundlagen der Mathematik 20, 47-48, 1974.

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