An analogue of Hilbert's 10th problem for fields of meromorphic functions over non-Archimedean valued fields
نویسندگان
چکیده
منابع مشابه
An analogue of Hilbert’s 10th problem for fields of meromorphic functions over non-Archimedean valued fields
Let K be a complete and algebraically closed valued field of characteristic 0. We prove that the set of rational integers is positive existentially definable in the field M of meromorphic functions on K in the language L z of rings augmented by a constant symbol for the independent variable z and by a symbol for the unary relation ‘‘the function x takes the value 0 at 0’’. Consequently, we prov...
متن کاملAn analogue of Hilbert’s tenth problem for fields of meromorphic functions over non-Archimedean valued fields
Let K be a complete and algebraically closed valued field of characteristic 0. We prove that the set of rational integers is positive existentially definable in the field M of meromorphic functions on K in the language Lz of rings augmented by a constant symbol for the independent variable z and by a symbol for the unary relation “the function x takes the value 0 at 0”. Consequently, we prove t...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2003
ISSN: 0022-314X
DOI: 10.1016/s0022-314x(03)00016-7