Characterizing integers among rational numbers with a universal-existential formula

American Journal of Mathematics

Volumn 131, Issue 3, 2009, Pages 675-682

  Poonen, Bjorn ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 68149153190     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.0.0057     Document Type: Article

References (8)

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2. [CZ07] G. Cornelissen and K. Zahidi, Elliptic divisibility sequences and undecidable problems about rational points, J. Reine Angew. Math. 613 (2007), 1-33.
3. [DPR61] M. Davis, H. Putnam, and J. Robinson, The decision problem for exponential diophantine equations, Ann. of Math. (2) 74 (1961), 425-436; MR 0133227 (24 #A3061).
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5. [Mat70] Yu. Matiyasevich, The Diophantineness of enumerable sets, Dokl. Akad. Nauk SSSR 191 (1970), 279-282 (Russian); MR 0258744 (41 #3390).
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7. [Ser73] J.-P. Serre, A Course in Arithmetic, Springer-Verlag, New York, 1973; Translated from the French; Grad. Texts in Math., no. 7; MR 0344216 (49 #8956).
8. [Shl07] A. Shlapentokh, Hilbert's Tenth Problem: Diophantine Classes and Extensions to Global Fields, Cambridge University Press, Cambridge, UK, 2007.