Related papers: Quantifier elimination for quasi-real closed field…
We work with semi-algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.
We develop a mathematical theory of quantization of multidimensional variational principles, and compare it with traditional constructions of quantum field theory. We conjecture that mathematical realization of quantum field theory axioms,…
Chevalley's theorem on the images of morphisms of schemes and the principle of quantifier elimination for the theory of algebraically closed fields are widely understood to be two perspectives on the same theorem. In this paper, we…
We describe a new quantifier elimination algorithm for real closed fields based on Thom encoding and sign determination. The complexity of this algorithm is elementary recursive and its proof of correctness is completely algebraic. In…
Quantifier-elimination or model-completeness of the affine part of some classical first order theories are proved.
Elimination of quantifiers is shown to fail dramatically for a group of well-known mathematical theories (classically enjoying the property) against a wide range of relevant logical backgrounds. Furthermore, it is suggested that only by…
In this paper we show if R is a filtered ring then we can define a quasi valuation. And if R is some kind of filtered ring then we can define a valuation. Then we prove some properties and relations for R.
Quantum field theory unifies concepts from quantum theory and from special relativity. Its mathematically rigorous description is quite intricate and is only partially understood; this is particularly true for the construction of operators…
We consider the expansion of the real field by the group of rational points of an elliptic curve over the rational numbers. We prove a completeness result, followed by a quantifier elimination result. Moreover we show that open sets…
A definable set in a pair (K, k) of algebraically closed fields is co-analyzable relative to the subfield k of the pair if and only if it is almost internal to k. To prove this and some related results for tame pairs of real closed fields…
We present a new procedure for quantizing field theory models on a noncommutative spacetime. The new quantization depends on the noncommutative parameter explicitly and reduces to the canonical quantization in the commutative limit. It is…
Quantifier elimination (QE) is an important problem that has numerous applications. Unfortunately, QE is computationally very hard. Earlier we introduced a generalization of QE called $\mathit{partial}$ QE (or PQE for short). PQE allows to…
Let $R$ be an o-minimal expansion of a group in a language in which $\textrm{Th}(R)$ eliminates quantifiers, and let $C$ be a predicate for a valuational cut in $R$. We identify a condition that implies quantifier elimination for…
A new approach is demonstrated that QFTs can be UV finite if they are viewed as the low energy effective theories of a fundamental underlying theory (that is complete and well-defined in all respects) according to the nowaday's standard…
The object of the present is a proof of the existence of functorial resolution of tame quotient singularities for quasi-projective varieties over algebraically closed fields.
Quantifier elimination over the reals is a central problem in computational real algebraic geometry, polynomial system solving and symbolic computation. Given a semi-algebraic formula (whose atoms are polynomial constraints) with…
We prove coherence of relatively quasi-free algebras over noetherian rings. Chase criterion for coherence is used.
The theory of valued difference fields $(K, \sigma, v)$ depends on how the valuation $v$ interacts with the automorphism $\sigma$. Two special cases have already been worked out - the isometric case, where $v(\sigma(x)) = v(x)$ for all…
We give an explicit algebraic characterisation of all definable henselian valuations on a dp-minimal real field. Additionally we characterise all dp-minimal real fields that admit a definable henselian valuation with real closed residue…
We study quasi-semisimple elements of disconnected reductive algebraic groups over an algebraically closed field. We describe their centralizers, define isolated and quasi-isolated quasi-semisimple elements and classify their conjugacy…