Diophantine definability over non-finitely generated non-degenerate modules of algebraic extensions of ℚ
Archive for Mathematical Logic 40 (4):297-328 (2001)
Abstract
We investigate the issues of Diophantine definability over the non-finitely generated version of non-degenerate modules contained in the infinite algebraic extensions of the rational numbers. In particular, we show the following. Let k be a number field and let K inf be a normal algebraic, possibly infinite, extension of k such that k has a normal extension L linearly disjoint from K inf over k. Assume L is totally real and K inf is totally complex. Let M inf be a non-degenerate O k -module, possibly non-finitely generated and contained in O Kinf . Then M inf contains a submodule M¯ inf such that M inf /M¯ inf is torsion and O k has a Diophantine definition over M¯ infAuthor's Profile
DOI
10.1007/pl00003843
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References found in this work
Questions of decidability and undecidability in number theory.B. Mazur - 1994 - Journal of Symbolic Logic 59 (2):353-371.
Diophantine undecidability in some rings of algebraic numbers of totally real infinite extensions of Q.Alexandra Shlapentokh - 1994 - Annals of Pure and Applied Logic 68 (3):299-325.
