Definitions
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 adv. In an elementary way.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adv. in an elementary manner
Etymologies
Examples

(In the case of a complete theory, the models of different cardinality will be elementarily equivalent, even if they are nonisomorphic).

Recalling that a complete theory T is one in which any sentence s, or its negation Not (s), belongs to the theory T, it follows that every model of a complete theory must be elementarily equivalent.

Whilst isomorphic models must be elementarily equivalent, there is no need for elementarily equivalent models to be isomorphic.

Two models of a theory are defined to be elementarily equivalent if they share the same truthvalues for all the sentences of the language.

The class of models of a complete theory will be mutually nonisomorphic, but they will nevertheless be elementarily equivalent.

In this case, the models of the theory will be mutually nonisomorphic and elementarily inequivalent.

Hence, mathematical logic suggests that the application of mathematical physics to the universe as a whole can generate two different types of multiverse: classes of nonisomorphic but elementarily equivalent models; and classes of nonisomorphic and elementarily inequivalent models.

If two structures are isomorphic then they share all modeltheoretic properties; in particular they are elementarily equivalent.

This description implied among other things that the structures elementarily equivalent to R are exactly the realclosed fields, a class of fields which was already known to the algebraists in its own right.

B are elementarily equivalent if and only if they have ultrapowers that are isomorphic to each other.
oroboros commented on the word elementarily
Sounds like the letters L M N T R L E.
May 17, 2008