Large cardinals and strong model theoretic transfer properties
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- by Matthew Foreman
- Trans. Amer. Math. Soc. 272 (1982), 427-463
- DOI: https://doi.org/10.1090/S0002-9947-1982-0662045-X
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Abstract:
In this paper we prove the following theorem: $[{\rm {Con}}({\rm {ZFC}} {\rm { + }} there is a {\rm {2 - }}huge cardinal) \Rightarrow for all n$ \[ {\rm {Con}}({\rm {ZFC + }}({\aleph _{n + 3}},{\aleph _{n + 2}},{\aleph _{n + 1}}) \twoheadrightarrow ({\aleph _{n + 2}},{\aleph _{n + 1}},{\aleph _n}))\]. We do this by using iterated forcing to collapse the $2$-huge cardinal to ${\aleph _{n + 1}}$ and extending the elementary embedding generically.References
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Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 272 (1982), 427-463
- MSC: Primary 03C55; Secondary 03E35, 03E55
- DOI: https://doi.org/10.1090/S0002-9947-1982-0662045-X
- MathSciNet review: 662045