The intersection number for forcing notions

Andrés F. Uribe-Zapata

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arXiv · 2401.14552

The intersection number for forcing notions

Andrés F. Uribe-Zapata

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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 $\mu$-intersection-linked, prove some of its basic properties, and provide some interesting examples.

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Andrés F. Uribe-Zapata. 2024-01-25. The intersection number for forcing notions. https://arxiv.org/abs/2401.14552

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