Relative elimination of quantifiers for Henselian valued fields

Ax, 1971, A metamathematical approach to some problems in number theory, AMS Proc. Symp. Pure Math., 20, 161, 10.1090/pspum/020/0316419 Ax, 1965, Diophantine problems over local fields I, Amer. J. Math., 87, 605, 10.2307/2373065 Ax, 1965, Diophantine problems over local fields II, Amer. J. Math., 87, 631, 10.2307/2373066 Ax, 1966, Diophantine problems over local fields III, Decidable fields, Ann. Math., 83, 437, 10.2307/1970476 Basarab, 1973, Some metamathematical aspects of the theory of Henselian fields, Studii Cercetǎri Matematice, 25, 1449 Basarab, 1978, Some model theory for Henselian valued fields, J. Algebra, 55, 191, 10.1016/0021-8693(78)90217-X Basarab, 1979, A model-theoretic transfer theorem for Henselian valued fields, J. Reine Angew. Math., 311/312, 1 Basarab, 1979, Model-theoretic methods in the theory of Henselian valued fields I, Studii Cercetǎri Matematice, 31, 3 Basarab, 1979, Model-theoretic methods in the theory of Henselian valued fields II, Studii Cercetǎri Matematice, 31, 617 Bourbaki, 1971, Commutative Algebra Cantor, 1984, On diophantine equations over the ring of all algebraic integers, J. Number Theory, 18, 1, 10.1016/0022-314X(84)90038-6 Chang, 1973, Model Theory, 73 Cherlin, 1983, Real closed rings II. Model theory, Ann. Pure Appl. Logic, 25, 213, 10.1016/0168-0072(83)90019-2 Cohen, 1969, Decision procedures for real and p-adic fields, Comm. Pure Appl. Math., 22, 131, 10.1002/cpa.3160220202 Delon, 1981, Quelques proprietés des corps valués en théorie des modèles, Thèse Denef, 1984, The rationality of the Poincaré series associated to the p-adic points on a variety, Invent. Math., 77, 1, 10.1007/BF01389133 Ershov, 1965, On the elementary theory of maximal valued fields, Algebra i Logika Sem., 4, 31 Ershov, 1966, On the elementary theory of maximal valued fields II, Algebra i Logika Sem., 5, 5 Ershov, 1967, On the elementary theory of maximal valued fields III, Algebra i Logika Sem., 6, 31 Ershov, 1967, On rational points over Henselian fields, Algebra i Logika Sem., 6, 39 Kochen, 1975, The model theory of local fields, 499, 384 Lang, 1965 Macintyre, 1976, On definable subsets of p-adic fields, J. Symbolic Logic, 41, 605, 10.2307/2272038 Prestel, 1984, Formally p-adic Fields,, 1050 Ribenroim, 1968 Robinson, 1968, Problems and methods in model theory, Lecture Notes, Varrena, CIME, 183 Robinson, 1970, Elementary embeddings of fields of power series, J. Number Theory, 2, 237, 10.1016/0022-314X(70)90024-7 Robinson, 1960, Elementary properties of ordered Abelian groups, Trans. Amer. Math. Soc., 96, 222, 10.1090/S0002-9947-1960-0114855-0 P. Roquette, Some tendencies in contemporary algebra, to appear. Sacks, 1972 L. van den Dries, Elementary invariants for Henselian valuation rings of mixed characteristics Manuscript notes. Weispfenning, 1976, On the elementary theory of Hensel fields, Ann. Math. Logic, 10, 59, 10.1016/0003-4843(76)90025-5 Weispfenning, 1978 V. Weispfenning, Quantifier elimination and decision procedures for valued fields, in: Logic Colloquium, Aachen 1983, Lecture Notes in Math., to appear. Ziegler, 1972