WordNet records no synonym and no antonym for forgetfulness. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
tendency to forget
unawareness caused by neglectful or heedless failure to remember
“his forgetfulness increased as he grew older”
Synonyms, antonyms and the broader and narrower relations for forgetfulness come from Princeton University’s WordNet. Full sources and licences.