2021/08/08 by Saharon Shelah, Shelah, Saharon
Mathematics · Medicine · #Advanced Topology and Set Theory #FOS: Mathematics #Ginkgo biloba and Cashew Applications #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2108.03666
openalex publication_date 2021/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a revised version (of late 2020) of [Sh:700], which is arXiv:math/0012170 . First point is noting that the proof of Theorem 4.3 in [Sh:700], which says that the proof giving the consistency \mathfrakb = \mathfrakd = \mathfraku < \mathfraka also gives \mathfraks = \mathfrakd . The proof uses a measurable cardinal and a c.c.c. forcing so it gives large \mathfrakd and assumes a large cardinal. Second point is adding to the results of \S2,\S3 which say that (in \S3 with no large cardinals) we can force ℵ1 < \mathfrakb = \mathfrakd < \mathfraka. We like to have ℵ1 < \mathfraks ≤ \mathfrakb = \mathfrakd < \mathfraka . For this we allow in \S2,\S3 the sets Kt to be uncountable; this requires non-essential changes. In particular, we replace usually ℵ0, ℵ1 by σ, ∂ . Naturally we can deal with \mathfraki and similar invariants. Third we proofread the work again. To get \mathfraks we could have retained the countability of the member of the It-s but the parameters would change with A ∈ It, well for a cofinal set of them; but the present seems simpler. We intend to continue in [Sh:F2009].