Omitting Types Theorem and Infinite Combinatrics

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400190
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: University of Tsukuba
• Principal Investigator: TSUBOI Akito 筑波大学, 数理物質系, 教授 (30180045)
• Co-Investigator(Renkei-kenkyūsha): TAKEUCHI Kota 筑波大学, 数理物質系数学域, 助教 (50722485)
• Research Collaborator: YANAGAWA Makoto 筑波大学, 数理物質科学研究科 ; YODA Hiroki 筑波大学, 数理物質科学研究科 ; OKABE Shunsuke 神戸大学, 大学院システム情報学研究科
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 数理論理学 / モデル理論

Outline of Final Research Achievements

Using Compactness Theorem, which is an important tool in model theory, we studied mathematical structures from model theoretic view point. Mathematical structures we studied are graph structures, models of arithmetic (PA or weaker systems) and models of o-minimal theories. As for the graph structures, we obtained results related to model completeness and sufficient conditions for the existence of a model companion. We also studied infinite combinatorics related to the problem of edge coloring of infinite graphs.

Free Research Field

モデル理論