The intersection number for forcing notions
Abstract
Based on works of Saharon Shelah, Jakob Kellner, and Anda T\u{a}nasie 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 -intersection-linked, prove some of its basic properties, and provide some interesting examples.
Keywords
Cite
@article{arxiv.2401.14552,
title = {The intersection number for forcing notions},
author = {Andrés F. Uribe-Zapata},
journal= {arXiv preprint arXiv:2401.14552},
year = {2024}
}
Comments
17 pages, conference paper to appear in Proceedings of RIMS Set Theory Workshop 2023. arXiv admin note: text overlap with arXiv:2312.13443