Set-theoretic aspects of phenomena from real analysis

• Project/Area Number: 25K07101
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12030:Basic mathematics-related
• Research Institution: Kobe University
• Principal Investigator: Brendle Jorg 神戸大学, システム情報学研究科, 教授 (70301851)
• Co-Investigator(Kenkyū-buntansha): メヒア ディエゴ 神戸大学, システム情報学研究科, 准教授 (70777961)
• Project Period (FY): 2025-04-01 – 2028-03-31
• Project Status: Granted (Fiscal Year 2025)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2027: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2026: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2025: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 数理論理学 / 集合論 / 強制法の理論 / 実解析

Outline of Research at the Start

We will investigate set-theoretic aspects of some phenomena from real analysis, like measure theory, Baire category, and density of sets of natural numbers. Particular focus will be on the order relationship between cardinal numbers describing these phenomena. For showing that no such order relationships exist, we will use forcing theory to carry out independence proofs.