elementary substructure造句

• So isolated types will be realized in every elementary substructure or extension.
• N \, is an elementary substructure of M \, by the Tarski Vaught test.
• The part of the theorem asserting that a structure has elementary substructures of all smaller infinite cardinalities is known as the "'downward L鰓enheim Skolem Theorem " '.
• In fact, S \ subset { \ mathcal P } ( X ) is stationary if and only if for any such structure M there is an elementary substructure of M that belongs to S.
• The downward L鰓enheim Skolem theorem gives a countable elementary substructure for any infinite first-order structure; the upward L鰓enheim Skolem theorem gives elementary extensions of any infinite first-order structure of arbitrarily large cardinality.
• An elementary substructure is a very special case of this; in particular an elementary substructure satisfies exactly the same first-order sentences as the original structure ( its "'elementary extension "').
• An elementary substructure is a very special case of this; in particular an elementary substructure satisfies exactly the same first-order sentences as the original structure ( its "'elementary extension "').
• There are also coherent motions at much smaller scales such as hairpin vortices and typical eddies, which are typically known as coherent substructures, as in coherent structures which can be broken up into smaller more elementary substructures.
• To see the connection with model theory, notice that if M is a universe X in a countable language and F is a Skolem function for M, then a stationary S must contain an elementary substructure of M.
• He is known for the Tarski Vaught test for elementary substructures, the Feferman Vaught theorem, the A
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   Vaught test for completeness and decidability, the Vaught two-cardinal theorem, and his conjecture on the nonfinite axiomatizability of totally categorical theories ( this work eventually led to geometric stability theory ).