Definitions
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- adverb In an
elementary way.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
- adverb in an elementary manner
Etymologies
from Wiktionary, Creative Commons Attribution/Share-Alike License
Support
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Examples
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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.
Archive 2009-06-01 Gordon McCabe 2009
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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.
Archive 2009-06-01 Gordon McCabe 2009
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The class of models of a complete theory will be mutually non-isomorphic, but they will nevertheless be elementarily equivalent.
Mathematical logic and multiverses Gordon McCabe 2009
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Whilst isomorphic models must be elementarily equivalent, there is no need for elementarily equivalent models to be isomorphic.
Archive 2009-06-01 Gordon McCabe 2009
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In this case, the models of the theory will be mutually non-isomorphic and elementarily inequivalent.
Mathematical logic and multiverses Gordon McCabe 2009
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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.
Mathematical logic and multiverses Gordon McCabe 2009
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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.
Mathematical logic and multiverses Gordon McCabe 2009
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(In the case of a complete theory, the models of different cardinality will be elementarily equivalent, even if they are non-isomorphic).
Mathematical logic and multiverses Gordon McCabe 2009
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Whilst isomorphic models must be elementarily equivalent, there is no need for elementarily equivalent models to be isomorphic.
Mathematical logic and multiverses Gordon McCabe 2009
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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.
Mathematical logic and multiverses Gordon McCabe 2009
oroboros commented on the word elementarily
Sounds like the letters L M N T R L E.
May 17, 2008