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Life on the Range

In A. Torza (ed.), Quantifiers, Quantifiers, and Quantifiers. Synthese LIbrary (forthcoming)

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  1. On the General Interpretation of First-Order Quantifiers.G. Aldo Antonelli - 2013 - Review of Symbolic Logic 6 (4):637-658.
    While second-order quantifiers have long been known to admit nonstandard, or interpretations, first-order quantifiers (when properly viewed as predicates of predicates) also allow a kind of interpretation that does not presuppose the full power-set of that interpretationgeneralā€ interpretations for (unary) first-order quantifiers in a general setting, emphasizing the effects of imposing various further constraints that the interpretation is to satisfy.
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