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On the elimination of some higher type quantifiers
Published online by Cambridge University Press: 09 January 2002
Abstract
This paper concerns the elimination of higher type quantifiers and gives two theorems. The first theorem shows that quantifiers in formulae of a specific form can be eliminated. The second theorem shows that quantifiers in formulae of a similar form cannot be eliminated, that is, such formulae do not have an equivalent first-order formula. The proof is based on the Ehrenfeucht game. These theorems are important for design of an interpreter of a ν act, which is a representation of mathematical action. Moreover, even if the universe is assumed to be finite, these theorems hold.
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- 2001 Cambridge University Press