Indenumerability and substitutional quantification

Notre Dame Journal of Formal Logic 23 (4):358-366 (1982)
We here establish two theorems which refute a pair of what we believe to be plausible assumptions about differences between objectual and substitutional quantification. The assumptions (roughly stated) are as follows: (1) there is at least one set d and denumerable first order language L such that d is the domain set of no interpretation of L in which objectual and substitutional quantification coincide. (2) There exist interpreted, denumerable, first order languages K with indenumerable domains such that substitutional quantification deviates from objectual quantification in K and this deviance remains for all name extensions I of K. We show these assumptions have actually been made, and then prove the refuting theorems.
Keywords objectual quantification  substitutional quantification
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DOI 10.1305/ndjfl/1093870148
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