On an Interpretation of Second Order Quantification in First Order Intuitionistic Propositional Logic

@article{Pitts1992OnAI,
  title={On an Interpretation of Second Order Quantification in First Order Intuitionistic Propositional Logic},
  author={Andrew M. Pitts},
  journal={J. Symb. Log.},
  year={1992},
  volume={57},
  pages={33-52}
}
We prove the following surprising property of Heyting's intuitionistic propositional calculus, IpC. Consider the collection of formulas, , built up from propositional variables (p; q; r; : : :) and falsity (?) using conjunction (^), disjunction (_) and implication (!). Write ` to indicate that such a formula is intuitionistically valid. We show that for each variable p and formula there exists a formula A p (e ectively computable from ), containing only variables not equal to p which occur in… CONTINUE READING
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