Skip to main content Accessibility help
×
Home

Prototypes for definable subsets of algebraically closed valued fields

  • Jan E. Holly (a1)

Abstract

Elimination of imaginaries for 1-variable definable equivalence relations is proved for a theory of algebraically closed valued fields with new sorts for the disc spaces. The proof is constructive, and is based upon a new framework for proving elimination of imaginaries, in terms of prototypes which form a canonical family of formulas for defining each set that is definable with parameters. The proof also depends upon the formal development of the tree-like structure of valued fields, in terms of valued trees, and a decomposition of valued trees which is used in the coding of certain sets of discs.

Copyright

References

Hide All
[1]Ax, James and Kochen, Simon, Diophantine problems over local fields, III, Annals of Mathematics, vol. 83 (1966), pp. 437456.
[2]Delon, Françoise, Espaces ultramétriques, this Journal, vol. 49 (1984), pp. 405424.
[3]van den Dries, Lou, Algebraic theories with definable Skolem functions, this Journal, vol. 49 (1984), pp. 625629.
[4]Haskell, Deirdre and Macpherson, Dugald, Cell decompositions of C-minimal structures, Annals of Pure and Applied Logic, vol. 66 (1994), pp. 113162.
[5]Holly, Jan E., Definable equivalence relations and disc spaces of algebraically closed valued fields, Ph.D. thesis, University of Illinois, 1992.
[6]Holly, Jan E., Definable operations on sets and elimination of imaginaries, Proceedings of the American Mathematical Society, vol. 117 (1993), pp. 11491157.
[7]Holly, Jan E., Canonical forms for definable subsets of algebraically closed and real closed valued fields, this Journal, vol. 60 (1995), pp. 843860.
[8]Macintyre, Angus, On definable subsets of p-adic fields, this Journal, vol. 41 (1976), pp. 605610.
[9]Macintyre, Angus, McKenna, Kenneth, and van den Dries, Lou, Elimination of quantifiers in algebraic structures, Advances in Mathematics, vol. 47 (1983), pp. 7487.
[10]Poizat, Bruno, Une théorie de Galois imaginaire, this Journal, vol. 48 (1983), pp. 11511170.
[11]Rammal, R., Toulouse, G., and Virasoro, M. A., Ultrametricity for physicists, Reviews of Modern Physics, vol. 58 (1986), pp. 765788.
[12]Robinson, Abraham, Complete theories, North-Holland, Amsterdam, 1956.
[13]Scowcroft, Philip, Equivalence relations on the p-adic line, Abstracts of Papers Presented to the American Mathematical Society, vol. 16 (1995), p. 15.
[14]Scowcroft, Philip and Macintyre, Angus, On the elimination of imaginaries from certain valued fields, Annals of Pure and Applied Logic, vol. 61 (1993), pp. 241276.

Prototypes for definable subsets of algebraically closed valued fields

  • Jan E. Holly (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed