Rocky Mountain Journal of Mathematics

The Boolean space of ${\bf R}$-places

Katarzyna Osiak

Full-text: Open access

Article information

Rocky Mountain J. Math., Volume 40, Number 6 (2010), 2003-2011.

First available in Project Euclid: 11 January 2011

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 12D15: Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx]
Secondary: 14P05: Real algebraic sets [See also 12D15, 13J30]

Real places spaces of real places


Osiak, Katarzyna. The Boolean space of ${\bf R}$-places. Rocky Mountain J. Math. 40 (2010), no. 6, 2003--2011. doi:10.1216/RMJ-2010-40-6-2003.

Export citation


  • E. Becker and D. Gondard, Notes on the space of real places of a formally real field, in Real analytic algebraic geometry, W. de Gruyter, Berlin, 1995%), 21-46.
  • E. Becker, J. Harman and A. Rosenberg, Signatures of fields and extension theory, J. Reine angew. Math. 330 (1982), 53-75.
  • T.C. Craven, The Boolean space of orderings of the field, Trans. Amer. Math. Soc. 209, (1975), 225-235.
  • –––, The topological space of orderings of rational function field, Duke Math. J. 41 (1974), 339-347.
  • D.W. Dubois, Infinite primes and ordered field, Dissert. Math. 69, (1970), 1-43.
  • Y.L. Ershov, The number of linear orders on a field, Math. Z. 6, (1969), 201-211; Math. Notes 6 (1969), 577–582 (in English).
  • D. Gondard and M. Marshall, Towards an abstract description of the space of real places, Contemp. Math. 253 (2000), 77-113.
  • T.Y. Lam, Orderings, valuations and quadratic forms, CBMS Regional Conf. Ser. Math. 52,. Published for the Conf. Board of the Math. Sciences, American Mathematical Society, Washington, D.C., %by AMS, 1983.
  • K. Osiak, A Cantor cube as a space of higher level orderings, Tatra Mt. Math. Publ. 32 (2005), 71-84.