The intersection number for forcing notions

Abstract

Based on works of Saharon Shelah, Jakob Kellner, and Anda Tănasie for controlling the cardinal characteristics of the continuum in ccc forcing extensions, in the author's master's thesis was introduced a new combinatorial notion: the intersection number for forcing notions, which was used in such thesis to build a general theory of iterated forcing using finitely additive measures. In this paper, we present the definition of such a notion and prove some of its fundamental properties in detail. Additionally, we introduce a new linkedness property called $\mu$-intersection-linked, prove some of its basic properties, and provide some interesting examples.

17 pages, conference paper to appear in Proceedings of RIMS Set Theory Workshop 2023. arXiv admin note: text overlap with arXiv:2312.13443