On a question of Abraham Robinson's

Preprint English OPEN
Koenigsmann, Jochen;
(2013)
  • Subject: Mathematics - Logic | 12L05, 12E30
    arxiv: Computer Science::Formal Languages and Automata Theory | Computer Science::Logic in Computer Science

In this note we give a negative answer to Abraham Robinson's question whether a finitely generated extension of an undecidable field is always undecidable. We construct 'natural' undecidable fields of transcendence degree 1 over Q all of whose proper finite extensions a... View more
  • References (12)
    12 references, page 1 of 2

    [CDM] Gregory Cherlin, Lou van den Dries, Angus Macintyre, The elementary theory of regularly closed fields, manuscript, 1980.

    [FJ] Michael Fried, Moshe Jarden, Field Arithmetic, Springer 1986, 3rd edition (revised by Moshe Jarden) 2008.

    [FV] Michael Fried, Helmuth V¨olklein, The embedding problem over a Hilbertian PAC-field, Ann. Math. 135 (1992), 469-481.

    [GPR] Barry Green, Florian Pop, Peter Roquette, On Rumely's local-global principle, Jber. Dt. Math.-Verein. 97 (1995), 43-74.

    Zeitschr. 224 (1997), 555-556.

    Symb. Logic 67(3) (2002), 947-956.

    Anatoli Ivanovic Malcev, On the undecidability of the elementary theory of certain fields (Russian), Sibrisk. Math. Zurnal 1(1) (1960), 71-77.

    [MB] Laurent Moret-Bailly, Groupes de Picard et probl`emes de Skolem II, Ann. Sci. E´cole Norm. Sup. (4) 22 (1989), 181-194.

    [Pr] Alexander Prestel, Einfu¨hrung in die mathematische Logik und Modelltheorie, Vieweg 1986.

    Abraham Robinson, Metamathematical Problems, J. Symb. Logic 38(3) (1973), 500-516.

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