Related papers: Constructive Quantifier Elimination with a Focus o…
We investigate prime avoidance for an arbitrary set of prime ideals in a commutative ring. Various necessary and/or sufficient conditions for prime avoidance are given, which yield natural classes of infinite sets of primes that satisfy…
We prove a theorem of Hinich type on existence of a model structure on a category related by an adjunction to the category of differential graded modules over a graded commutative ring.
An example is constructed of a local ring and a module of finite type and finite projective dimension over that ring such that the module is not rigid. This shows that the rigidity conjecture is false.
We show that bounded type implies finite type for a constructible subcategory of the module category of a finitely generated algebra over a field, which is a variant of the first Brauer-Thrall conjecture. A full subcategory is constructible…
If $R$ is a commutative unital ring and $M$ is a unital $R$-module, then each element of $\operatorname{End}_R(M)$ determines a left $\operatorname{End}_{R}(M)[X]$-module structure on $\operatorname{End}_{R}(M)$, where…
We introduce a procedure for proving safety properties. This procedure is based on a technique called Partial Quantifier Elimination (PQE). In contrast to complete quantifier elimination, in PQE, only a part of the formula is taken out of…
This paper investigates the possibility of constructive extraction of measurable selector from set-valued maps which may commonly arise in viability theory, optimal control, discontinuous systems etc. For instance, existence of solutions to…
We associate to every proof structure in multiplicative linear logic an ideal which represents the logical content of the proof as polynomial equations. We show how cut-elimination in multiplicative proof nets corresponds to instances of…
We consider the problem of elimination of existential quantifiers from a Boolean CNF formula. Our approach is based on the following observation. One can get rid of dependency on a set of variables of a quantified CNF formula F by adding…
In 1985, van den Dries showed that the theory of the reals with a predicate for the integer powers of two admits quantifier elimination in an expanded language, and is hence decidable. He gave a model-theoretic argument, which provides no…
Our aim is to construct fibrewise localizations in model categories. For pointed spaces, the general idea is to decompose the total space of a fibration as a diagram over the category of simplices of the base and replace it by the localized…
We generalize a recent result of Clausen: For a number field with integers O, we compute the K-theory of locally compact O-modules. For the rational integers this recovers Clausen's result as a special case. Our method of proof is quite…
Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…
In constructive algebra one cannot in general decide the irreducibility of a polynomial over a field K. This poses some problems to showing the existence of the algebraic closure of K. We give a possible constructive interpretation of the…
We prove that Z in definable in Q by a formula with 2 universal quantifiers followed by 7 existential quantifiers. It follows that there is no algorithm for deciding, given an algebraic family of Q-morphisms, whether there exists one that…
The replacement (or collection or choice) axiom scheme asserts bounded quantifier exchange. We prove the independence of this scheme from various weak theories of arithmetic, sometimes under a complexity assumption.
Computational materials design often profits from the fact that some complicated contributions are not calculated for the real material, but replaced by results of models. We turn this approximation into a very general and in principle…
We consider the use of Quantifier Elimination (QE) technology for automated reasoning in economics. QE dates back to Tarski's work in the 1940s with software to perform it dating to the 1970s. There is a great body of work considering its…
The framework of cyclic proof systems provides a reasonable proof system for logics with inductive definitions. It also offers an effective automated proof search procedure for such logics without finding induction hypotheses. Recent…
We prove some algebraic results on the ring of matrix differential operators over a differential field in the generality of non-commutative principal ideal rings. These results are used in the theory of non-local Poisson structures.