In accordance with truth or fact or reality (synset 400037620)
"she was now truly American"; "a genuinely open society"; "they don't really listen to us"
In actual fact (synset 400150568)
"to be nominally but not actually independent"; "no one actually saw the shark"; "large meteorites actually come from the asteroid belt"synonym: actually
In fact (used as intensifiers or sentence modifiers) (synset 400038407)
"in truth, moral decay hastened the decline of the Roman Empire"; "really, you shouldn't have done it"; "a truly awful book"domain usage: intensifier, intensive - a modifier that has little meaning except to intensify the meaning it modifies
Used as intensifiers;
`real' is sometimes used informally for `really';
`rattling' is informal (synset 400032295)"she was very gifted"; "he played very well"; "a really enjoyable evening"; "I'm real sorry about it"; "a rattling good yarn"