COMPLETENESS AND CATEGORICITY (IN POWER): FORMALIZATION WITHOUT FOUNDATIONALISM*

@article{Baldwin2014COMPLETENESSAC,
  title={COMPLETENESS AND CATEGORICITY (IN POWER): FORMALIZATION WITHOUT FOUNDATIONALISM*},
  author={John T. Baldwin},
  journal={The Bulletin of Symbolic Logic},
  year={2014},
  volume={20},
  pages={39 - 79}
}
  • J. Baldwin
  • Published 1 March 2014
  • Philosophy, Mathematics
  • The Bulletin of Symbolic Logic
Abstract We propose a criterion to regard a property of a theory (in first or second order logic) as virtuous: the property must have significant mathematical consequences for the theory (or its models). We then rehearse results of Ajtai, Marek, Magidor, H. Friedman and Solovay to argue that for second order logic, ‘categoricity’ has little virtue. For first order logic, categoricity is trivial; but ‘categoricity in power’ has enormous structural consequences for any of the theories satisfying… 
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On Formalism Freeness: Implementing Gödel's 1946 Princeton Bicentennial Lecture
  • J. Kennedy
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