Quantifier Elimination in Fields
نویسندگان
چکیده
Here we give a detailed description of the quantifier elimination algorithm for algebraically closed fields (ACF); We also describe its implementation in the system AFC-EQ that was developed in GIS Group for Inteligent Systems on the Faculty of Mathematics, University of Belgrade.
منابع مشابه
Quantifier Elimination and Real Closed Ordered Fields with a Predicate for the Powers of Two
In this thesis we first review the model theory of quantifier elimination and investigate the logical relations among various quantifier elimination tests. In particular we prove the equivalence of two quantifier elimination tests for countable theories. Next we give a procedure for eliminating quantifiers for the theory of real closed ordered fields with a predicate for the powers of two. This...
متن کاملQuantifier elimination for the theory of algebraically closed valued fields with analytic structure
The theory of algebraically closed non-Archimedean valued fields is proved to eliminate quantifiers in an analytic language similar to the one used by Cluckers, Lipshitz and Robinson. The proof makes use of a uniform parameterized normalization theorem which is also proved in this paper and which has far reaching consequences in the geometry of definable sets. This method of proving quantifier ...
متن کاملQuantifier Elimination on Real Closed Fields and Differential Equations
This paper surveys some recent applications of quantifier elimination on real closed fields in the context of differential equations. Although polynomial vector fields give rise to solutions involving the exponential and other transcendental functions in general, many questions can be settled within the real closed field without referring to the real exponential field. The technique of quantifi...
متن کاملQuantifier Elimination following Muchnik
This paper describes a very simple (high school level) algorithm of quantifier elimination for real closed fields and algebraically closed fields following an idea of A. Muchnik. The algorithm essentially relies on intermediate value property, pseudo-euclidean division and sign change table for univariate polynomials over R. Surprisingly this algorithm exhibits some more general feature and it ...
متن کاملQuantifier Elimination in Tame Infinite p-ADIC Fields
We give an answer to the question as to whether quantifier elimination is possible in some infinite algebraic extensions of Qp (‘infinite p-adic fields’) using a natural language extension. The present paper deals with those infinite p-adic fields which admit only tamely ramified algebraic extensions (so-called tame fields). In the case of tame fields whose residue fields satisfy Kaplansky’s co...
متن کاملQuantifier Elimination in p-adic Fields
We present a tutorial survey of quantifier-elimination and decision procedures in p-adic :fieIds. The p-adic :fieIds are studied in the (so-called) P,,-formalism of Angus Macintyre, for whieh motivation is provided through a rieh body of analogies with real-closed :fields. Quantifier-elimination and decision procedures are described proceeding via a Cylindrical Algebraic Decomposition of affine...
متن کامل