On Ø-definable elements in a field

• Autores: Apoloniusz Tyszka
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 58, Fasc. 1, 2007, págs. 73-84
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We develop an arithmetic characterization of elements in a field which are firstorder definable by a parameterfree existential formula in the language of rings. As applications we show that in fields containing an algebraically closed field only the elements of the prime field are existentially ;definable. On the other hand, many finitely generated extensions of Q contain existentially ;definable elements which are transcendental over Q. Finally, we show that all transcendental elements inRhaving a recursive approximation by rationals, are definable in R(t), and the same holds when one replaces R by any Pythagorean subfield of R

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