The theory of inductive, existentially closed and forcing companions and positively existentially closed models

Project type: Grant funding of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan

Code of the project: АР055135285 (01.01.2018 – 31.12.2020)

Title: The theory of inductive, existentially closed and forcing companions and positively existentially closed models.

The object of research, development or design: Companions, companion theories, existentially closed structures.

Aim of work: Further development of the theory of existential closure and the study of important related concepts such as the forcing – method and inductive companions. Formation of new directions and issues. The study of formulas and theories of low quantifier complexity.

Research methods: To achieve the goal and solve research problems, new approaches are being developed – the study of the classical issues of model theory, by studying the class of final models of a suitable model. New concepts and original methods and techniques of proof are introduced – a companion of the model, a companion of the theory and a forcing method for studying them. The invaluable role played by the methods of Roland Frase. As the experience has already shown, in the theory of existential closeness the fundamental role is played by the concept of “maximum existential type” introduced by A.Nurtazin. Also, the development of many questions in the classes of abelian groups and commutative rings greatly simplifies their solution in the general case.

Field of application: Model theory, algebra.

Project Investigator: Nurtazin A.T. (IICT CS MES RK).

The organization – executor: IICT CS MES RK.