Adjective : an elementary grammar. ,elementary teachers.    From Dictionary.com. 

A and B are elementarily equivalent if and only if Th (A) = Th (B).    From Wordnik.com.  [First-order Model Theory] Reference

If there is an elementary embedding from A to B then A and B are elementarily equivalent.    From Wordnik.com.  [First-order Model Theory] Reference

B are elementarily equivalent if and only if they have ultrapowers that are isomorphic to each other.    From Wordnik.com.  [First-order Model Theory] Reference

In this case, the models of the theory will be mutually non-isomorphic and elementarily inequivalent.    From Wordnik.com.  [Mathematical logic and multiverses] Reference

Two L-structures that are models of exactly the same sentences of L are said to be elementarily equivalent.    From Wordnik.com.  [First-order Model Theory] Reference

Whilst isomorphic models must be elementarily equivalent, there is no need for elementarily equivalent models to be isomorphic.    From Wordnik.com.  [Mathematical logic and multiverses] Reference

If two structures are isomorphic then they share all model-theoretic properties; in particular they are elementarily equivalent.    From Wordnik.com.  [First-order Model Theory] Reference

The class of models of a complete theory will be mutually non-isomorphic, but they will nevertheless be elementarily equivalent.    From Wordnik.com.  [Mathematical logic and multiverses] Reference

On the other hand an embedding between elementarily equivalent structures, or even between isomorphic structures, need not be elementary.    From Wordnik.com.  [First-order Model Theory] Reference

(In the case of a complete theory, the models of different cardinality will be elementarily equivalent, even if they are non-isomorphic).    From Wordnik.com.  [Mathematical logic and multiverses] Reference

Two models of a theory are defined to be elementarily equivalent if they share the same truth-values for all the sentences of the language.    From Wordnik.com.  [Mathematical logic and multiverses] Reference

It investigates them, tries them and punishes them elementarily, but the perpetrators of bloody crimes do not receive any publicity in our society.    From Wordnik.com.  [FIDEL CASTGRO ADDRESSES MININT ANNIVERSARY CEREM] Reference

To continue the example of the field R of real numbers: It is often not at all obvious whether two given structures are or are not elementarily equivalent.    From Wordnik.com.  [First-order Model Theory] Reference

For instance, a predicative function of an individual variable must have order 1 (in current terminology, it is elementarily definable and quantifies only over individuals).    From Wordnik.com.  [Paradoxes and Contemporary Logic] Reference

The Queen is not conceited; she is aware there are many things she cannot understand, and she likes to have them explained to her elementarily, not at length and in detail, but shortly and clearly.    From Wordnik.com.  [Queen Victoria Story of Her Life and Reign, 1819-1901] Reference

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.    From Wordnik.com.  [Mathematical logic and multiverses] Reference

This description implied among other things that the structures elementarily equivalent to R are exactly the real-closed fields, a class of fields which was already known to the algebraists in its own right.    From Wordnik.com.  [First-order Model Theory] Reference

The whole world will surely have a common language, that is quite elementarily Utopian, and since we are free of the trammels of convincing story-telling, we may suppose that language to be sufficiently our own to understand.    From Wordnik.com.  [A Modern Utopia] Reference

When you dehydrate by alcohol 100 grammes of the embryo of wheat, obtained by the same means as the membrane (a process indicated later on), this embryo, treated with ether, produces 20 grammes of oils composed elementarily of hydrogen, oxygen, carbon, azote, sulphur, and phosphorus.    From Wordnik.com.  [Scientific American Supplement, No. 275, April 9, 1881] Reference

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 non-isomorphic but elementarily equivalent models; and classes of non-isomorphic and elementarily inequivalent models.    From Wordnik.com.  [Mathematical logic and multiverses] Reference

I find so much that cannot be explained elementarily, or anything near it.    From Wordnik.com.  [Personal Recollections, from Early Life to Old Age, of Mary Somerville] Reference

The whole world will surely have a common language, that is quite elementarily.    From Wordnik.com.  [A Modern Utopia] Reference

Cutting and pasting proves that you can function elementarily in Microsoft Windows.    From Wordnik.com.  [Denver Post: News: Breaking: Local] Reference

At most, they are didactic inclusions whose only real value is to elementarily graze upon issues that have existed and have been eternally discussed and debated in other venues and forms of media.    From Wordnik.com.  [Twitch] Reference

Queen, "said Melbourne -- who knew of what he was speaking, if any statesman then did --" is not conceited; she is aware there are many things she cannot understand, and likes them explained to her elementarily, not at length and in detail, but shortly and clearly. ".    From Wordnik.com.  [Great Britain and Her Queen] Reference

I think I show it you more accurately in the robin's back than I could in any other bird; its mode of transition into more brilliant color is, in him, elementarily simple; and although there is nothing, or rather because there is nothing, in his plumage, of interest like that of tropical birds, or even of our own game-birds, I think it will be desirable for you to learn first from the breast of the robin what a feather is.    From Wordnik.com.  [Love's Meinie Three Lectures on Greek and English Birds] Reference

Not that the spiral form actually adds to the strength of a Lombardic pillar, by imitating contortions of wood, any more than the fluting of a Doric shaft adds to its strength by imitating the canaliculation of a reed; but the perfect action of the imagination, which had adopted the encircling acanthus for the capital, adopted the twining stemma for the shaft; the pure delight of the eye being the first condition in either case: and it is inconceivable how much of the pleasure taken both in ornament and in natural form is founded elementarily on groups of spiral line.    From Wordnik.com.  [Proserpina, Volume 1 Studies Of Wayside Flowers] Reference

"Intrinsically, inherently, fundamentally, elementarily, primarily.    From Wordnik.com.  [The Color of Her Panties]