Logicism, quantifiers, and abstraction

With the aid of a non-standard (but still first-order) cardinality quantifier and an extra-logical operator representing numerical abstraction, this paper presents a formalization of first-order arithmetic, in which numbers are abstracta of the equinumerosity relation, their properties derived from those of the cardinality quantifier and the abstraction operator.
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M. Kary (2009). (Math, Science, ?). Axiomathes 19 (3):61-86.

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