I apologize for asking the same question twice, since my last question was not really understood and there seems to be a problem preventing me from comment of editing the question.


Is there a model of ZFC such that:


1. Every OD set of reals is measurable.
2. Every OD ${\hspace{.03 in}\it family}$ of sets of reals contains at least one OD definable set.


Thank you



Definable families of sets of reals
The answer to this question also is negative. (I take statement 2 to be only about non-empty families.) 


First, your statement 2 implies that every real is ordinal definable, since the set of singletons of non-OD reals is definable, but can't have any OD member. 


In particular, your statement 2 implies that there is a definable well-ordering of the reals, without assuming AC, using the HOD order. 


Second, your statement 2 implies that every set of reals is ordinal definable, since the collection of non-ordinal definable sets of reals is a definable family, but has no ordinal-definable members. 


But this contradicts statement 1, since we can define a non-measurable set using the Vitali argument.


