Real Analysis Exchange
- Real Anal. Exchange
- Volume 27, Number 1 (2001), 335-340.
Hausdorff Dimension, Analytic Sets and Transcendence
Every analytic real closed proper sub-field of $\mathbb R$ has Hausdorff dimension zero. Equivalently, every analytic set of real numbers having positive Hausdorff dimension contains a transcendence base for $\mathbb R$.
Real Anal. Exchange, Volume 27, Number 1 (2001), 335-340.
First available in Project Euclid: 6 June 2008
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 28A78: Hausdorff and packing measures 03C64: Model theory of ordered structures; o-minimality 03E15: Descriptive set theory [See also 28A05, 54H05] 12L12: Model theory [See also 03C60]
Edgar, G. A.; Miller, Chris. Hausdorff Dimension, Analytic Sets and Transcendence. Real Anal. Exchange 27 (2001), no. 1, 335--340. https://projecteuclid.org/euclid.rae/1212763973