Compactness in Singular Cardinals Revisited

Authors

  • Saharon Shelah

DOI:

https://doi.org/10.5644/SJM.15.02.05

Keywords:

set theory, group theory, almost free groups, almost free algebras, varieties

Abstract

This is the second combinatorial proof of the compactness theorem for singular from 1977. In fact it gives a somewhat stronger theorem.

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References

Shai Ben David, On Shelah's compactness of cardinals, Israel J. Math. 31 (1978), 34--56 and 394.

Keith J. Devlin and Saharon Shelah, A weak version of $diamondsuit $ which follows from $2^{aleph _{0}}<2^{aleph _{1}}$, Israel J. Math. 29 (1978), 239--247.

Paul C. Eklof, On singular compactness, Algebra Universalis, 14 (1982), no.~3, 310--316.

William G. Fleissner, Questions, 1977, preprint.

Wilfrid Hodges, For singular $lambda$, $lambda$-free, implies free. Algebra Universalis, 12 (1981), 205--220.

David W. Kueker, Countable approximations and Lowenheim-Skolem theorems, Ann. Math. Logic, 11 (1977), 57--103.

Saharon Shelah, Dependent dreams: recounting types, arxiv:1202.5795.

---------------- Note on a min-max problem of Leo Moser, J. Combin. Theory, 6 (1969), 298--300.

---------------- A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals, Israel J. Math. 21 (1975), 319--349.

---------------- A combinatorial proof of the singular compactness theorem. Now 266, Mimeograph notes and lecture in a mini-conference, Berlin, 'August', 77 (1977).

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Published

12.02.2020

How to Cite

Shelah, S. . (2020). Compactness in Singular Cardinals Revisited. Sarajevo Journal of Mathematics, 15(2), 201–208. https://doi.org/10.5644/SJM.15.02.05

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