What is the highest degree held by Freeman Dyson?

According to both Freeman Dyson's homepage at the IAS and the accompanying C.V., he never earned another degree after his B.A. While unusual, this was much more possible at the time, since research in general was less well supported and organized. A number of other notable contemporaneous researchers (e.g., Ed Fredkin) also never earned a doctorate.

In the modern world, this is much more difficult, though similar recognition can be obtained as, e.g., a Professor of Practice.

The Cambridge University Annual Register for 1968-69 (which is the only copy I have to hand) records just a Bachelor of Arts degree awarded in 1945 to FJ Dyson of Trinity College. (At Cambridge the BA degree is awarded for studies in sciences not just arts subjects.) He would have been qualified for the award of the Master of Arts degree without any further academic work or examinations. The University website explains that "if you hold a Cambridge BA, you may proceed to the MA not less than six years from the end of your first term of residence, providing that you have held your BA degree for at least two years." Many BA graduates do not bother to take the MA degree. Nevertheless for formal purposes at Cambridge the MA degree is regarded as ranking higher even than master's degrees awarded for actual academic work.