According to sources in the gaming world, Kotaku has reported that the PlayStation 4 will not use Sony's Cell processor nor any possible successor. As we all remember, Sony developed the current cell processor in combination with Toshiba and IBM at the tune of 1 Billion Dollars. The report further states that following a Forbes report, That AMD would not only be working on the PS4's Processor, but also it's graphics card.
The Cell processor was not the technological feat that Sony had hoped it would be. Many developers complained at its release that it was "very difficult to program for" and that it had a "high learning curve." Which could explain why the PS3 took 18 months to find its stride in great games. This being said, it is hard to know if it was the cell processor underperforming, or a conscience decision by developers to program in such a way to make it easier to port from the PS3 to the 360 and vice versa.
It will be very interesting to see how these rumors pan out.