All uncountable cardinals can be singular
- M. Gitik
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Assuming the consistency of the existence of arbitrarily large strongly compact cardinals, we prove the consistency with ZF of the statement that every infinite set is a countable union of sets of smaller cardinality. Some other statements related to this one are investigated too.
- K. Devlin and R. Jensen,Marginalia to a theorem of Silver, in Proc. Internat. Summer Institute and Logic Colloq., Lecture Notes in Math.499, Springer-Verlag, Berlin, 1975, pp. 115–143.
- J. Dodd and R. Jensen,The core model, handwritten notes.
- U. Felgner,Comparison of the axioms of local and universal choice, Fund. Math.71 (1971), 73–62.
- T. J. Jech,Lectures in set theory with particular emphasis on the method of forcing, Lecture Notes in Mathematics217, Springer-Verlag, Berlin, 1971, p. 137.
- T. J. Jech,The Axiom of Choice, North-Holland, Amsterdam, 1977.
- A. Levy,Independence results in set theory by Cohen's Method IV (abstract), Notices Amer. Math. Soc.10 (1963), 592–593.
- A. Levy,Definability in Axiomatic Set Theory II, inMath Logic and Formulations of Set Theory, Proc. Internat. Colloq. (J. Bar-Hillel, ed.), North-Holland, Amsterdam, 1970, pp. 129–145.
- K. Prikry,Changing measurable, Dissertationes Math.68 (1970), 5–52.
- J. R. Shoenfield,Unramified forcing in ‘Axiomatic Set Theory’, Proc. Symposia in Pure Math.13 (D. Scott, ed.), Providence, Rhode Island, 1971, pp. 351–382.
- E. Speker,Zur Axiomatik der Mengenlehre, Z. Math. Logik Grundlagen Math.3 (1957), 173–210. CrossRef
- All uncountable cardinals can be singular
Israel Journal of Mathematics
Volume 35, Issue 1-2 , pp 61-88
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- M. Gitik (1)
- Author Affiliations
- 1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel