A set of axioms for nonstandard extensions | Zendy

Dasgupta Abhijit | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

A set of axioms for nonstandard extensions

Author(s) -

Dasgupta Abhijit

Publication year - 2011

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.201010025

Subject(s) - finitary , axiom , mathematics , partial function , set (abstract data type) , construct (python library) , algebra over a field , axiom of choice , characterization (materials science) , algebraic number , axiomatic system , algebraic structure , order (exchange) , discrete mathematics , pure mathematics , set theory , computer science , programming language , mathematical analysis , materials science , geometry , nanotechnology , finance , economics

We give an axiomatic characterization for complete elementary extensions, that is, elementary extensions of the first‐order structure consisting of all finitary relations and functions on the underlying set. Such axiom systems have been studied using various types of primitive notions (e.g., [1, 3, 6]). Our system uses the notion of partial functions as primitive. Properties of nonstandard extensions are derived from five axioms in a rather algebraic way, without the use of metamathematical notions such as formulas or satisfaction. For example, when applied to the real number system, it provides a complete framework for developing nonstandard analysis based on hyperreals without having to construct them and without any use of logic. This has possible pedagogical and expository applications as presented in, e.g., [5], [6]. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research