M . Aiguier F . Barbier An institution - independent Proof of the Beth Definability Theorem

An Institution-independent Proof of the Beth Definability Theorem

The Basic Theorem and its Consequences

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...

Beth Definability in Institutions

BETH DEFINABILITY IN INSTITUTIONS MARIUS PETRIA∗ AND RĂZVAN DIACONESCU Abstract. This paper studies definability within the theory of institutions, a version of abstract model This paper studies definability within the theory of institutions, a version of abstract model theory that emerged in computing science studies of software specification and semantics. We generalise the concept of definab...

A new proof for the Banach-Zarecki theorem: A light on integrability and continuity

To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

An Isomorphism Between Monoids of External Embeddings: About Definability in Arithmetic

We use a new version of the Definability Theorem of Beth in order to unify classical Theorems of Yuri Matiyasevich and Jan Denef in one structural statement. We give similar forms for other important definability results from Arithmetic and Number Theory. A.M.S. Classification: Primary 03B99; Secondary 11D99.