Discussion On The Related Properties Of Real Field

Algebraic model theory is an important branch of model theory.Algebraic model theory has been widely used in many branches of mathematics.The real domain is an important part of it.According to the unique form of the Hilbert 17 th question,E.Artin and O.Schreier discovered the basic properties of the real number field and its subdomains,and introduced these basic properties into the domain domain to establish the famous Artin-Schreier theory.Since the real domain has considerable The universality,and the applicability of theories and methods are also quite extensive,so the research on the real domain has been carried out in depth,and many achievements have been obtained.This paper uses the real-domain order,the real domain and the concept of the real closed domain and related properties.Exploring the relationship between real and positive cones,ideals,and semi-algebraic sets.The specific arrangements are as follows:1.Explain the development history of model theory and real domain theory,as well as the basic knowledge required for this dissertation.2.Introduce the concept of the real domain,the real domain and the real closed domain concept and related properties.3.According to the order nature of the real domain,the related properties of the positive cone in the real domain are discussed.4.Discuss ideal related applications in the real world.5.Exploring the relationship between real and semi-algebraic sets.