Heyting Research System And Its Related Properties

Steven Vikers has proposed the topological system in his work Topology via Logic by synthesizing the methods of topology and the theory of logics, which also is applied to study of computer’s theory. Firstly,with the help of the idea of topological systems and the properties enjoyed by Frame structures and Heyting algebras, the new algebras system-Heyting system is put forward that takes the Heyting algebras as its principal body; Secondly, a suitable method connecting Heyting systems is established which is called H-continuous mapping; Thirdly, the representation of H-spatialization of a Heyting system is given, and related properties are investigated. The research methods of heyting algebras and the research contents of topological system are enriched with the work of this paper.the construction of chapters and the concrete contents of this paper are as follows:Chapter1:Preliminaries. This chapter provides the knowledge prepared to the full text. The basic concepts of lattice,complete lattice,distributed lattice,Frame, Heyting algebra.Heyting algebra homomorphism,topological system, spatializition and localification of topological systems are given.Chapter2:Heyting Systems with thier morphisms.Firstly,with the help of the idea of topological systems and the properties enjoyed by Frame structures and Heyting algebras, the new algebras system-Heyting system is put forward that takes the Heyting algebras as its principal body; Secondly, a suitable method connecting Heyting systems is established which is called H-continuous mapping; Thirdly, it is proved that the content taking Heyting systems as objects, H-continuous mapping as morphisms is a category.Chapter3:Heyting System and its Representation by H-Spatislization. On the basis of Heyting System established in last chapter,the representation of H-spatialization of a Heyting system is given, and related properties are investigated by means of the ideas and methods of topological systems.Chapter4:Heyting System and its Representation by H-localization.Based on the theory of Heyting system and by means of the ideas and methods of topological systems it is put forword that the representation of H-localization of a Heyting system in this chapter.Besides.the related properties are researched. This chapter enriches ehe theory of Heyting system as the parallel section of the last one.