The GPS carrier-phase ambiguity problem will be considered, first with the existing two frequencies at 1575.42 MHz. And 1227.6 MHz. And then with the addition of the newly proposed third frequency at 1176.45 MHz. Special emphases will be placed on understanding the benefits and limitations of forming various linear combinations of the measurements. A discussion of what a better third frequency or even a fourth frequency could provide will also be included. The factors, which limit the baseline separation distance between reference and user receivers, will also be addressed and methods for extending the baseline distances will be discussed.