Categoricity and Consistency in Second-Order Logic |
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Authors: | Jouko Väänänen |
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Affiliation: | 1. University of Helsinki, Finland;2. University of Amsterdam, Netherlands.jouko.vaananen@helsinki.fi |
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Abstract: | We analyse the concept of a second-order characterisable structure and divide this concept into two parts—consistency and categoricity—with different strength and nature. We argue that categorical characterisation of mathematical structures in second-order logic is meaningful and possible without assuming that the semantics of second-order logic is defined in set theory. This extends also to the so-called Henkin structures. |
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