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### A Remark on Henkin Sentences and Their Contraries

John P. Burgess
Source: Notre Dame J. Formal Logic Volume 44, Number 3 (2003), 185-188.

#### Abstract

That the result of flipping quantifiers and negating what comes after, applied to branching-quantifier sentences, is not equivalent to the negation of the original has been known for as long as such sentences have been studied. It is here pointed out that this syntactic operation fails in the strongest possible sense to correspond to any operation on classes of models.

First Page:
Primary Subjects: 03C80
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1091030856
Digital Object Identifier: doi:10.1305/ndjfl/1091030856
Mathematical Reviews number (MathSciNet): MR2130790
Zentralblatt MATH identifier: 02187148

### References

[1] Caicedo, X., and M. Krynicki, "Quantifiers for reasoning with imperfect information and $\Sigma\sp 1\sb 1$"-logic, pp. 17--31 in Advances in Contemporary Logic and Computer Science (Salvador, 1996), edited by W. A. Carnielli, vol. 235 of Contemporary Mathematics, American Mathematical Society, Providence, 1999.
Mathematical Reviews (MathSciNet): MR2001b:03037
Zentralblatt MATH: 0935.03048
[2] Enderton, H. B., "Finite partially-ordered quantifiers", Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 16 (1970), pp. 393--97.
Mathematical Reviews (MathSciNet): MR44:1546
Zentralblatt MATH: 0193.29405
Digital Object Identifier: doi:10.1002/malq.19700160802
[3] Hintikka, J., The Principles of Mathematics Revisited, Cambridge University Press, Cambridge, 1996.
Mathematical Reviews (MathSciNet): MR97j:03005
Zentralblatt MATH: 0869.03003
[4] Walkoe, W. J., Jr., "Finite partially-ordered quantification", The Journal of Symbolic Logic, vol. 35 (1970), pp. 535--55.
Mathematical Reviews (MathSciNet): MR43:4646
Zentralblatt MATH: 0219.02008
Digital Object Identifier: doi:10.2307/2271440
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