caa a22 4500 388039485 CHVBK 20180307125017.0 cr unu---uuuuu 161130e199803 xx s 000 0 eng 10.2307/2586598 doi S0022481200015437 pii (NATIONALLICENCE)cambridge-10.2307/2586598 Undecidable wreath products and skew power series fields [Elektronische Daten] We prove the undecidability of a very large class of restricted and unrestricted wreath products (Theorem 1.2), and of some skew fields of power series (Section2). Both undecidabilities are obtained by interpreting some enrichments of twisted wreath products, which are themselves proved to be undecidable (Proposition 1.1). We consider division rings of power series in various languages: We show (Theorem 2.8) that every power series division ring k((B)), whose field of constants k is commutative and whose ordered group of exponents is noncommutative with a convex center, is undecidable in every extension of the language of rings where the valuation and the ordered group B are definable. For certain k and B we prove here the undecidability of the structure where X↾ k((B))xB is the restriction of the multiplication to k((B)) Χ B,and γ is a given conjugation of k((B)). This shows that we cannot hope to improve our previous result, a sort of Ax-Kochen-Ershov principle for power series division rings, which ensures that is decidable for every decidable solvable B. Copyright © Association for Symbolic Logic 1998 undecidable groups nationallicence undecidable fields nationallicence wreath products nationallicence power series division rings nationallicence Delon Françoise Équipe de Logique Mathématique de Paris VII, 2, Place Jussieu—Case 7012, 75251 Paris Cedex 05, France, E-mail: delon@logique.jussieu.fr Simonetta Patrick Équipe de Logique Mathématique de Paris VII, 2, Place Jussieu—Case 7012, 75251 Paris Cedex 05, France, E-mail: simbaud@logique.jussieu.fr The Journal of Symbolic Logic Cambridge University Press 63/1(1998-03), 237-246 0022-4812 63:1<237 1998 63 JSL https://doi.org/10.2307/2586598 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586598 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Delon Françoise Équipe de Logique Mathématique de Paris VII, 2, Place Jussieu—Case 7012, 75251 Paris Cedex 05, France, E-mail: delon@logique.jussieu.fr NATIONALLICENCE 700 1- Simonetta Patrick Équipe de Logique Mathématique de Paris VII, 2, Place Jussieu—Case 7012, 75251 Paris Cedex 05, France, E-mail: simbaud@logique.jussieu.fr NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/1(1998-03), 237-246 0022-4812 63:1<237 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge