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Talk:Indescribable cardinal

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First-order indescribable with

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Is this definition conventional? Cf. e.g. Kanamori 2003 p.58. --Fourier-Deligne Transgirl (talk) 15:56, 4 May 2023 (UTC)[reply]

The paper "Infinitary Compactness without Strong Inaccessibility" (Boos, 1976) defines it using , but in that paper it's denoted . C7XWiki (talk) 22:31, 11 September 2023 (UTC)[reply]

Forcing comparisons of the least - and -indescribable cardinals

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Let denote the least -indescribable cardinal and denote the least -indescribable cardinal. Theorem 7.1 (p.148) in Huaser's thesis "Independence Results for Indescribable Cardinals" (1989) seems to state that for any function with domain and codomain , there is a model of ZFC+GCH in which, for all and , if , and if . I don't know enough about forcing to be sure that this is a consistency result, but if anyone can confirm it may be a good thing to add under the Properties section. C7XWiki (talk) 01:47, 8 September 2023 (UTC)[reply]