@article{012e856d37bd4c82b843af340c4fddb1,
title = "Dimension of definable sets, algebraic boundedness and Henselian fields",
author = "{Van den Dries}, Lou",
note = "Funding Information: Definition. Let 5e be a full Tarski system on the nonempty set A. Then a dimension function on 6e is a function d:t._J,~ b°m--* {--oo} t.J N such that for all sets S, $1, $2 e 6era, m >I O, we have: (Dim 1) d(S) = -oo¢¢,S =0, d({a}) = 0 for each a cA, d(A 1) = 1. (Dim 2) d(S1 t3 $2) = max(d(S1), d(S2)). (Dim 3) d(S °) = d(S) for each permutation o of {1 .... , m}, where S ° = {(xo(1) .... , Xo(m)) • A m : (Xl .... , Xm) • S}. (Dim 4) Let T e 5e,,,+l and put T~ = {y e A : (x, y) e T) for each x •A m, and * This work was partially supported by an NSF-grant. 0168-0072/89/$3.50 {\textcopyright} 1989, Elsevier Science Publishers B.V. (North-Holland)",
year = "1989",
month = dec,
day = "12",
doi = "10.1016/0168-0072(89)90061-4",
language = "English (US)",
volume = "45",
pages = "189--209",
journal = "Annals of Pure and Applied Logic",
issn = "0168-0072",
publisher = "Elsevier B.V.",
number = "2 PART 1",
}