Modern logic, useful and interesting like chess competitions of mentally disabled persons

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Dec 18, 2021, 6:38:52 AM12/18/21
"Finally, as Gödel observes, his argument is restricted to countable vocabularies; Henkin proves the results for uncountable languages. [...] Henkin (Corollary 2) uses the uncountable vocabulary to deduce the full force of the Löwenheim-Skolem-Tarski theorem: a consistent first order theory has models in every infinite cardinality. [...] Henkin already points out that his proof (unlike Gödel's) generalizes easily to uncountable vocabularies. [...] McKinsey (also noting the uncountable application) and Heyting give straightforward accounts in Mathematical Reviews of the result of Henkin's papers on first order and theory of types respectively with no comments on the significance of the result. Still more striking, Ackermann's review of Henkin's proof gives a routine summary of the new argument and concludes with 'The reviewer can not follow the author when he speaks of an extension to an uncountable set of relation symbols, since such a system of notations can not exist'." [John Baldwin: "The explanatory power of a new proof: Henkin's completeness proof" (25 Feb 2017)]

Ackermann's clear and correct position seems "striking". Logic has really become a perverted subject – useful and interesting like chess competitions of mentally disabled persons!

Regards, WM

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