Related papers: Affinization and quantifier-elimination
We give a sufficient condition for quantising integrable systems.
We study the model theory of the ring of adeles of a number field. We obtain quantifier elimination results in the language of rings and some enrichments. We given consequences for definable subsets of the adeles, and their measures.
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
Gravity does not naturally fit well with canonical quantization. Affine quantization is an alternative procedure that is similar to canonical quantization but may offer a positive result when canonical quantization fails to offer a positive…
We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.
We give a sufficient condition for a model theoretic structure $B$ to 'inherit' quantifier elimination from another structure $A$. This yields an alternative proof of one of the main result from \cite{kle}, namely quantifier elimination for…
Affine quantization is a relatively new procedure, and it can solve many new problems. This essay reviews this new, and novel, procedure for particle problems, as well as those of fields and gravity. New quantization tools, which are…
Discussed is the quantized version of the classical description of collective and internal affine modes as developed in Part I. We perform the Schr\"odinger quantization and reduce effectively the quantized problem from $n^{2}$ to $n$…
Fine's influential Canonicity Theorem states that if a modal logic is determined by a first-order definable class of Kripke frames, then it is valid in its canonical frames. This article reviews the background and context of this result,…
We prove quantifier elimination for the theory of quasi-real closed fields with a compatible valuation. This unifies the same known results for algebraically closed valued fields and real closed valued fields.
We describe a method for inverting Gentzen's cut-elimination in classical first-order logic. Our algorithm is based on first computign a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize…
The cofinality quantifiers were introduced by Shelah as an example of a compact logic stronger than first-order logic. We show that the classes of models axiomatized by these quantifiers can be turned into an Abstract Elementary Class by…
We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
Let $L$ be the language of rings. We provide an axiomatization of the $L$-theories of quaternions and octonions and characterize their models: they coincide, up to isomorphism, with quaternion and octonion algebras over a real closed field,…
Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set…
Two types of explanations have been receiving increased attention in the literature when analyzing the decisions made by classifiers. The first type explains why a decision was made and is known as a sufficient reason for the decision, also…
In this paper a constructive formalization of quantifier elimination is presented, based on a classical formalization by Tobias Nipkow. The formalization is implemented and verified in the programming language/proof assistant Agda. It is…
Ext-int.\ one affine functions are functions affine in the direction of one-divisible exterior forms, with respect to exterior product in one variable and with respect to interior product in the other. The purpose of this article is to…
We prove a highest weight theorem classifying irerducible finite--dimensional representations of quantum affine algebras and survey what is currently known about the structure of these representations.