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  • ARNO FEHM (a1)


In [1], Anscombe and Koenigsmann give an existential ∅-definition of the ring of formal power series F[[t]] in its quotient field in the case where F is finite. We extend their method in several directions to give general definability results for henselian valued fields with finite or pseudo-algebraically closed residue fields.



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[1]Anscombe, Will and Koenigsmann, Jochen, An existential ∅-definition of in , this Journal, vol. 79 (2014), no. 4, pp. 1336–1343.
[2]Ax, James, On the undecidability of power series fields. Proceedings of the American Mathematical Society, vol. 16 (1965), p. 846.
[3]Ax, James, The elementary theory of finite fields. Annals of Mathematics, vol. 88 (1968), no. 2, pp. 239271.
[4]Ax, James and Kochen, Simon, Diophantine problems over local fields I. American Journal of Mathematics, vol. 87 (1965), no. 3, pp. 605630.
[5]Cluckers, Raf, Derakhshan, Jamshid, Leenknegt, Eva, and Macintyre, Angus, Uniformly defining valuation rings in henselian valued fields with finite or pseudo-finite residue fields. Annals of Pure and Applied Logic, vol. 164 (2013), pp. 12361246.
[6]Efrat, Ido, Valuations, Orderings, and Milnor K-Theory, American Mathematical Society, Providence, 2006.
[7]Fehm, Arno, Subfields of ample fields. Rational maps and definability. Journal of Algebra, vol. 323 (2010), pp. 17381744.
[8]Fried, Michael D. and Jarden, Moshe, Field Arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol. 11, Springer, Berlin, 2008.
[9]Heinemann, B. and Prestel, A., Fields regularly closed with respect to finitely many valuations and orderings. Canadian Mathematical Society Conference Proceedings, vol. 4 (1984), pp. 297336.
[10]Helbig, Patrick, Existentielle Definierbarkeit von Bewertungsringen, Bachelor thesis, Konstanz, 2013.
[11]Prestel, Alexander, Jensen, R. B. and Prestel, A., editors, Pseudo real closed fields, Set Theory and Model Theory, Proceedings, Bonn 1979, Springer, Berlin, 1981, pp. 127156.



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