શરૂઆતમાં,

elementarily's Usage Examples:

notion for saturated models is that any "reasonably small" model of T is elementarily embedded in a saturated model, where "reasonably small" means cardinality.

the universe of sets start to look similar, in the sense that each is elementarily embeddable into a later one.

Since the theory is complete, all of its models are elementarily equivalent.

mathematical logic, two structures M and N of the same signature σ are called elementarily equivalent if they satisfy the same first-order σ-sentences.

Such groups are elementarily equivalent to the integers ( Z , + , < ) {\displaystyle (\mathbb {Z}.

The Bijou was the first theatre in the United States to be elementarily lighted by electricity, which Thomas Edison personally installed and.

torsion-free word-hyperbolic groups and to characterize all groups that are elementarily equivalent to (that is, have the same first-order theory as) a given.

support most everyday mathematics (via the addition of elementarily-expressible axioms such as Zermelo–Fraenkel set theory (ZFC)).

the field of real numbers and the field of real algebraic numbers are elementarily equivalent structures.

used to show that any two countable atomic models of a theory that are elementarily equivalent are isomorphic.

expressive enough to support most everyday mathematics (via the addition of elementarily-expressible axioms such as Zermelo–Fraenkel set theory (ZFC)).

Artin-Schreier theorem, the degree of this extension is necessarily 2, and F is elementarily equivalent to R.

generating a meta-level, set-theoretic falsehood, namely in relation to other elementarily-equivalent set-theories not identical to the one chosen.