FOM: infallible cardinals

john l. bell jbell at
Fri Jan 29 10:51:16 EST 1999

A notion very closely related to Joe Shipman's "infallible" cardinals
appeared (in essence at least) in "Natural Models of Set Theories," by
Montague and Vaught, Fundamenta Mathematicae, 1959. Call an ordinal k
impeccable if (V-sub-k, epsilon) is an elementary substructure of
(V,epsilon). (Clearly every impeccable cardinal is infallible.) Then
Montague and Vaught show that, for example, if an impeccable ordinal
exists, then the least one must be cofinal with omega, and so fails to be a
"large" cardinal in any of the usual intrinsic senses. 

--John Bell  

Professor John L. Bell
Department of Philosophy
University of Western Ontario
London, Ontario
Canada N6A 3K7

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