Abstract
In this paper I prove the following theorems which are the converses of some results of Judah and Laver (1983) and of Judah and Marshall (1993).
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-IfKM+ATW is not an extension by definition ofKM (and the model involved is well founded), then the existence of two inaccessible cardinals is consistent with ZF.
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-IfKM+ATW is not a conservative extension ofKM (and the model involved is well founded), then the existence of an inaccessible number of inaccessible cardinals is consistent with ZF.
whereKM is Kelley Morse theory andKM+ATW isKM with types of well-orders.
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References
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Research funded by Fondecyt 0762/92 and Fondecyt 1940695
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Marshall, M.V. Types in class set theory and inaccessible cardinals. Arch Math Logic 35, 145–156 (1996). https://doi.org/10.1007/BF01268615
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DOI: https://doi.org/10.1007/BF01268615