Categoricity and indefinite extensibility

Proceedings of the Aristotelian Society 102 (3):217–235 (2002)
Abstract
Structure is central to the realist view of mathematical disciplines with intended interpretations and categoricity is a model-theoretic notion that captures the idea of the determination of structure by theory. By considering the cases of arithmetic and (pure) set theory, I investigate how categoricity results might offer support from within to the realist view. I argue, amongst other things, that second-order quantification is essential to the support the categoricity results provide. I also note how the findings on categoricity relate to a fundamental feature of the realist position
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DOI 10.1111/j.0066-7372.2003.00052.x
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