Next: What is a CAD? Up: An overview of quantifier Previous: An overview of quantifier

Some conventions and notation

Throughout this thesis, , , and will be used to denote the integer, rational, and real rings respectively. For the remainder of this section it will always be assumed that is in prenex form (see [Mishra(1993)] p. 356 for a discussion of converting an arbitrary formula to prenex form). Specifically, it will be assumed that

where and is a quantifier free formula.

For any , the level of is defined as the largest such that . If is a set of polynomials, will denote the -level elements of .

Finally, the '' symbol will be used to denote evaluation, so if is a point in free-variable space, means evaluated at , as discussed in the previous section.

Christopher W Brown
2001-07-10