Cohen Preservation and Independence
| Autor: | Fischer, Vera, Switzer, Corey Bacal |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | We provide a general preservation theorem for preserving selective independent families along countable support iterations. The theorem gives a general framework for a number of results in the literature concerning models in which the independence number $\mathfrak{i}$ is strictly below $\mathfrak{c}$, including iterations of Sacks forcing, Miller partition forcing, $h$-perfect tree forcings, coding with perfect trees. Moreover, applying the theorem, we show that $\mathfrak{i} = \aleph_1$ in the Miller Lite model. An important aspect of the preservation theorem is the notion of "Cohen preservation", which we discuss in detail. Comment: 11 pages, submitted. arXiv admin note: text overlap with arXiv:2202.12046 |
| Databáze: | arXiv |
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