• of quantifier alternation are thought of as being simpler, with the quantifier-free formulas as the simplest. A theory has quantifier elimination if for...
    12 KB (1,435 words) - 13:58, 17 March 2025
  • there is an algorithm that, given a quantifier-free formula defining a semialgebraic set, produces a quantifier-free formula for its projection. In fact...
    21 KB (2,984 words) - 05:10, 2 May 2025
  • form, that is, a string of quantifiers and bound variables followed by a quantifier-free formula. Quantifier elimination is a concept of simplification...
    32 KB (4,559 words) - 12:11, 11 May 2025
  • viewed as the theory of the methods to make quantifier elimination algorithmically effective. Quantifier elimination over the reals is another example, which...
    5 KB (660 words) - 05:45, 25 January 2024
  • quantifier elimination, every definable subset of an algebraically closed field is definable by a quantifier-free formula in one variable. Quantifier-free...
    63 KB (9,065 words) - 10:26, 2 April 2025
  • \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...
    5 KB (615 words) - 17:55, 16 July 2021
  • with each quantifier block limited to j variables. '<' is considered to be quantifier-free; here, bounded quantifiers are counted as quantifiers. PA(1, j)...
    24 KB (3,249 words) - 21:25, 22 May 2025
  • named after Alfred Tarski and Abraham Seidenberg. It implies that quantifier elimination is possible over the reals, that is that every formula constructed...
    6 KB (754 words) - 04:48, 19 May 2025
  • Thumbnail for Time complexity
    Presburger arithmetic Computing a Gröbner basis (in the worst case) Quantifier elimination on real closed fields takes at least double exponential time, and...
    41 KB (5,003 words) - 04:16, 18 April 2025
  • garbage collection by reference counting[G60] and of the method of quantifier elimination by cylindrical algebraic decomposition.[G75] He received his PhD...
    4 KB (247 words) - 15:25, 25 April 2025
  • Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities....
    14 KB (2,492 words) - 00:49, 1 April 2025
  • In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least...
    11 KB (1,535 words) - 22:47, 14 December 2024
  • finite, then the Fraïssé limit of K {\displaystyle \mathbf {K} } has quantifier elimination. If the language of K {\displaystyle \mathbf {K} } is finite, and...
    10 KB (1,388 words) - 16:42, 3 March 2025
  • of quantifier elimination can be used to show that definable sets in particular theories cannot be too complicated. Tarski established quantifier elimination...
    69 KB (8,370 words) - 19:50, 19 April 2025
  • induction Binary decision diagrams DPLL Higher-order unification Quantifier elimination Alt-Ergo Automath CVC E IsaPlanner LCF Mizar NuPRL Paradox Prover9...
    28 KB (2,933 words) - 21:40, 29 March 2025
  • Tarski's quantifier elimination procedure for deciding statements in the first-order theory of the reals without the restriction to existential quantifiers. However...
    32 KB (3,821 words) - 10:57, 27 May 2025
  • Quantifier elimination. Current implementations of decision procedures for the theory of real closed fields are often based on quantifier elimination...
    4 KB (503 words) - 23:15, 25 April 2024
  • Cylindrical algebraic decomposition (category Quantifier (logic))
    double exponential complexity. CAD provides an effective version of quantifier elimination over the reals that has a much better computational complexity than...
    4 KB (430 words) - 09:24, 5 May 2024
  • theoretical study of the computational complexity of decidability and quantifier elimination in the first order theory of real numbers. The Sturm sequence and...
    19 KB (2,807 words) - 17:03, 2 July 2024
  • Kowloon, Hong Kong Queen Elizabeth Hospital, Adelaide, in Australia Quantifier elimination, a technique to simplify formulas Quadratic equation, an equation...
    2 KB (287 words) - 18:24, 17 April 2024
  • Thumbnail for Algebraic geometry
    with an acceptable complexity the Tarski–Seidenberg theorem on quantifier elimination over the real numbers. This theorem concerns the formulas of the...
    62 KB (7,498 words) - 11:10, 27 May 2025
  • Thumbnail for Angus Macintyre
    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...
    9 KB (889 words) - 15:25, 24 December 2024
  • 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...
    9 KB (1,092 words) - 21:37, 27 April 2025
  • 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...
    11 KB (1,294 words) - 21:21, 20 March 2024
  • any statement, either it or its negation is provable; have quantifier elimination; eliminate imaginaries; be finitely axiomatizable; be decidable: There...
    36 KB (5,269 words) - 20:51, 27 December 2024
  • Thumbnail for Negation
    Negation (redirect from Quantifier negation)
    are two quantifiers, one is the universal quantifier ∀ {\displaystyle \forall } (means "for all") and the other is the existential quantifier ∃ {\displaystyle...
    19 KB (2,236 words) - 02:31, 5 January 2025
  • developed to make the argument rigorous. 1931 Alfred Tarski's real quantifier elimination. Improved and popularized by Abraham Seidenberg in 1954. (Both use...
    26 KB (3,217 words) - 06:11, 27 January 2025
  • 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...
    13 KB (1,957 words) - 19:50, 25 May 2025
  • algebraic closure of F. The theory of algebraically closed fields has quantifier elimination. Shipman, J. Improving the Fundamental Theorem of Algebra The Mathematical...
    13 KB (1,838 words) - 18:02, 14 March 2025
  • parameters. The theory of R ≤ {\displaystyle {\mathcal {R}}^{\leq }} has quantifier elimination. Thus the definable sets are Boolean combinations of solutions to...
    8 KB (1,268 words) - 08:22, 21 May 2025