Basic Ideas
To show constructively that a theory has quantifier elimination, it suffices to show that we can eliminate an existential quantifier applied to a conjunction of literals, that is, show that each formula of the form:
where each is a literal, is equivalent to a quantifier-free formula. Indeed, suppose we know how to eliminate quantifiers from conjunctions of formulae, then if is a quantifier-free formula, we can write it in disjunctive normal form
and use the fact that
is equivalent to
Finally, to eliminate a universal quantifier
where is quantifier-free, we transform into disjunctive normal form, and use the fact that is equivalent to
Read more about this topic: Quantifier Elimination
Famous quotes containing the words basic and/or ideas:
“The gay world that flourished in the half-century between 1890 and the beginning of the Second World War, a highly visible, remarkably complex, and continually changing gay male world, took shape in New York City.... It is not supposed to have existed.”
—George Chauncey, U.S. educator, author. Gay New York: Gender, Urban Culture, and the Making of the Gay Male World, 1890-1940, p. 1, Basic Books (1994)
“She [Evelina] is a little angel!... Her face and person answer my most refined ideas of complete beauty.... She has the same gentleness in her manners, the same natural graces in her motions, that I formerly so much admired in her mother. Her character seems truly ingenuous and simple; and at the same time that nature has blessed her with an excellent understanding and great quickness of parts, she has a certain air of inexperience and innocency that is extremely interesting.”
—Frances Burney (1752–1840)