[FOM] Ordinal definable numbers

[Timothy Y. Chow]

Garabed Gulbenkian posed the following interesting question on 
MathOverflow.net which perhaps someone here on FOM can answer.

Is the following statement consistent with ZFC?

"There exists a denumerably infinite and ordinal definable set of real 
numbers, not all of whose elements are ordinal definable."

You can post your answer directly to MathOverflow.net:

http://mathoverflow.net/questions/17608/a-question-about-ordinal-definable-real-numbers

Tim