Forcing in Proof Theory

@article{Avigad2004ForcingIP,
  title={Forcing in Proof Theory},
  author={Jeremy Avigad},
  journal={Bulletin of Symbolic Logic},
  year={2004},
  volume={10},
  pages={305 - 333}
}
  • J. Avigad
  • Published 1 September 2004
  • Philosophy
  • Bulletin of Symbolic Logic
Abstract Paul Cohen's method of forcing, together with Saul Kripke's related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or… 
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