axiom of dependent choice

In mathematics, the axiom of dependent choices, denoted DC, is a weak form of the axiom of choice (AC) which is still sufficient to develop most of real analysis. Unlike full AC, DC is insufficient to prove (given ZF) that there is a nonmeasurable set of reals, or that there is a set of reals without the property of Baire or without the perfect set property.
See more at Wikipedia.org...