of quantifier alternation are thought of as being simpler, with the quantifier-free formulas as the simplest. A theory has quantifier elimination if for...

there is an algorithm that, given a quantifier-free formula defining a semialgebraic set, produces a quantifier-free formula for its projection. In fact...

viewed as the theory of the methods to make quantifier elimination algorithmically effective. Quantifier elimination over the reals is another example, which...

form, that is, a string of quantifiers and bound variables followed by a quantifier-free formula. Quantifier elimination is a concept of simplification...

quantifier elimination, every definable subset of an algebraically closed field is definable by a quantifier-free formula in one variable. Quantifier-free...

with each quantifier block limited to j variables. '<' is considered to be quantifier-free; here, bounded quantifiers are counted as quantifiers. PA(1, j)...

named after Alfred Tarski and Abraham Seidenberg. It implies that quantifier elimination is possible over the reals, that is that every formula constructed...

\ldots ,e^{x_{n}})=0.} Thus, while this theory does not have full quantifier elimination, formulae can be put in a particularly simple form. This result...

Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities....

Presburger arithmetic Computing a Gröbner basis (in the worst case) Quantifier elimination on real closed fields takes at least double exponential time, and...

garbage collection by reference counting[G60] and of the method of quantifier elimination by cylindrical algebraic decomposition.[G75] He received his PhD...

finite, then the Fraïssé limit of K {\displaystyle \mathbf {K} } has quantifier elimination. If the language of K {\displaystyle \mathbf {K} } is finite, and...

In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least...

Tarski's quantifier elimination procedure for deciding statements in the first-order theory of the reals without the restriction to existential quantifiers. However...

of quantifier elimination can be used to show that definable sets in particular theories cannot be too complicated. Tarski established quantifier elimination...

Quantifier elimination. Current implementations of decision procedures for the theory of real closed fields are often based on quantifier elimination...

double exponential complexity. CAD provides an effective version of quantifier elimination over the reals that has a much better computational complexity than...

with an acceptable complexity the Tarski–Seidenberg theorem on quantifier elimination over the real numbers. This theorem concerns the formulas of the...

induction Binary decision diagrams DPLL Higher-order unification Quantifier elimination Alt-Ergo Automath CVC E IsaPlanner LCF Mizar NuPRL Paradox Prover9...

theoretical study of the computational complexity of decidability and quantifier elimination in the first order theory of real numbers. The Sturm sequence and...

stability theory.[citation needed] In 1976, he proved a result on quantifier elimination for p-adic fields from which a theory of semi-algebraic and subanalytic...

Kowloon, Hong Kong Queen Elizabeth Hospital, Adelaide, in Australia Quantifier elimination, a technique to simplify formulas Quadratic equation, an equation...

intervals and points. O-minimality can be regarded as a weak form of quantifier elimination. A structure M is o-minimal if and only if every formula with one...

topology. Equivalently, a d-constructible set is the set of solutions to a quantifier-free, or atomic, formula with parameters in K. Like the theory of algebraically...

are two quantifiers, one is the universal quantifier ∀ {\displaystyle \forall } (means "for all") and the other is the existential quantifier ∃ {\displaystyle...

developed to make the argument rigorous. 1931 Alfred Tarski's real quantifier elimination. Improved and popularized by Abraham Seidenberg in 1954. (Both use...

algebraic closure of F. The theory of algebraically closed fields has quantifier elimination. Shipman, J. Improving the Fundamental Theorem of Algebra The Mathematical...

follows from the Feferman–Vaught theorem that can be shown using quantifier elimination. Another way of stating this is that first-order theory of positive...

any statement, either it or its negation is provable; have quantifier elimination; eliminate imaginaries; be finitely axiomatizable; be decidable: There...

parameters. The theory of R ≤ {\displaystyle {\mathcal {R}}^{\leq }} has quantifier elimination. Thus the definable sets are Boolean combinations of solutions to...