Erratum to “Infinite finitely generated fields are biinterpretable with ℕ”
Journal of the American Mathematical Society, Tome 24 (2011) no. 3, p. 917
There is a serious error in the valuation recovery argument in the paper Infinite finitely generated fields are biinterpretable with ${\mathbb N}$. Consequently, Pop’s Conjecture that elementarily equivalent finitely generated fields are isomorphic remains open.
@article{10_1090_S0894_0347_2011_00696_6,
author = {Scanlon, Thomas},
title = {Erratum to {{\textquotedblleft}Infinite} finitely generated fields are biinterpretable with {\ensuremath{\mathbb{N}}{\textquotedblright}}},
journal = {Journal of the American Mathematical Society},
pages = {917--917},
year = {2011},
volume = {24},
number = {3},
doi = {10.1090/S0894-0347-2011-00696-6},
url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-2011-00696-6/}
}
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%0 Journal Article %A Scanlon, Thomas %T Erratum to “Infinite finitely generated fields are biinterpretable with ℕ” %J Journal of the American Mathematical Society %D 2011 %P 917-917 %V 24 %N 3 %U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-2011-00696-6/ %R 10.1090/S0894-0347-2011-00696-6 %F 10_1090_S0894_0347_2011_00696_6
Scanlon, Thomas. Erratum to “Infinite finitely generated fields are biinterpretable with ℕ”. Journal of the American Mathematical Society, Tome 24 (2011) no. 3, p. 917. doi: 10.1090/S0894-0347-2011-00696-6
[1] Infinite finitely generated fields are biinterpretable with ℕ J. Amer. Math. Soc. 2008 893 908
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