Edward Adams' second wife, Abigail died before he did so she would not be mentioned by name, anyway, in his will. His will does make reference to his current wife, indicating he did indeed marry a third time after Abigail died. And indeed, in the Medfield Vital Records (p. 111), we find:
ADAMS, Edward, Ens., and Sarah Taylor, Jan. 6, 1709-10.
Vital records of Medfield, Massachusetts, to the year 1850,
Boston, MA: New-England Historic Genealogical Society: 1903