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Archive for Mathematical Logic

, Volume 41, Issue 6, pp 581–602 | Cite as

Transfer principles in nonstandard intuitionistic arithmetic

  • J. Avigad
  • J. Helzner

Abstract.

 Using a slight generalization, due to Palmgren, of sheaf semantics, we present a term-model construction that assigns a model to any first-order intuitionistic theory. A modification of this construction then assigns a nonstandard model to any theory of arithmetic, enabling us to reproduce conservation results of Moerdijk and Palmgren for nonstandard Heyting arithmetic. Internalizing the construction allows us to strengthen these results with additional transfer rules; we then show that even trivial transfer axioms or minor strengthenings of these rules destroy conservativity over HA. The analysis also shows that nonstandard HA has neither the disjunction property nor the explicit definability property. Finally, careful attention to the complexity of our definitions allows us to show that a certain weak fragment of intuitionistic nonstandard arithmetic is conservative over primitive recursive arithmetic.

Keywords

Careful Attention Conservation Result Slight Generalization Transfer Principle Transfer Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • J. Avigad
    • 1
  • J. Helzner
    • 1
  1. 1.Department of Philosophy, Carnegie Mellon University, 135 Baker Hall, Pittsburgh, PA 15213, USA. e-mail: avigad@cmu.eduUS

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