Fields of surreal numbers and exponentiation

Fundamenta Mathematicae

Volumn 167, Issue 2, 2001, Pages 173-188

  Van Den Dries, Lou ^a   Ehrlich, Philip ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b OHIO UNIVERSITY   (United States)

Author keywords

Exponential fields; Surreal numbers

Indexed keywords

EID: 0039843733     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: 10.4064/fm167-2-3     Document Type: Article

References (10)

1. J. Conway, On Numbers and Games, Academic Press, 1976.
2. L. van den Dries, Tame Topology and o-Minimal Structures, London Math. Soc. Lecture Note Ser. 248, Cambridge Univ. Press, 1998.
3. L. van den Dries, A. Macintyre and D. Marker, The elementary theory of restricted analytic fields with exponentiation, Ann. of Math. 140 (1994), 183-205.
4. P. Ehrlich, Number systems with simplicity hierarchies: a generalization of Conway's theory of surreal numbers, J. Symbolic Logic, to appear.
5. _, Absolutely saturated models, Fund. Math. 133 (1989), 41-46.
6. H. Gonshor, An Introduction to the Theory of Surreal Numbers, London Math. Soc. Lecture Note Ser. 110, Cambridge Univ. Press, 1986.
7. F. Hausdorff, Set Theory, Chelsea, New York, 1957.
8. J. Lurie, Review of [1], J. Symbolic Logic 63 (1998), 1602-1604.
9. A. Macintyre and A. Wilkie, On the decidability of the real exponential field, in: Kreiseliana, P. Odifreddi (ed.), A. K. Peters, Wellesley, MA, 1996, 441-467.
10. A. Wilkie, Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function, J. Amer. Math. Soc. 9 (1996), 1051-1094.