Related Concepts
Various model theoretic ideas are related to quantifier elimination, and there are various equivalent conditions.
Every theory with quantifier elimination is model complete.
A first-order theory T has quantifier elimination if and only if for any two models B and C of T and for any common substructure A of B and C, B and C are elementarily equivalent in the language of T augmented with constants from A. In fact, it is sufficient here to show that any sentence with only existential quantifiers have the same truth value in B and C.
Read more about this topic: Quantifier Elimination
Famous quotes containing the words related and/or concepts:
“The content of a thought depends on its external relations; on the way that the thought is related to the world, not on the way that it is related to other thoughts.”
—Jerry Alan Fodor (b. 1935)
“During our twenties...we act toward the new adulthood the way sociologists tell us new waves of immigrants acted on becoming Americans: we adopt the host culture’s values in an exaggerated and rigid fashion until we can rethink them and make them our own. Our idea of what adults are and what we’re supposed to be is composed of outdated childhood concepts brought forward.”
—Roger Gould (20th century)