<p>Barnard gets a Columbia diploma as all Columbia University students do. It will have “Barnard College” on it as well where Columbia College students will have “Columbia College” on it and as Fu students will have that indicated, and other divisions will have their names on the diploma, but it will all be under the umbrella of Columbia University.</p>
<p>The technical definition is the athletic league. The Ivy League is a term not just limited to those colleges. There are high schools who have traditionally, and continue to call their sports league the Ivy league. So yes, Barnard is in the Ivy League as the students play in that league. But in the context of colleges, it is the 8 schools. </p>
<p>I know some Harvard graduates who refer to their alma mater as Harvard College, rather than university. Strictly speaking, many universities have many divisions, including Harvard, that serve as a main umbrella but are not the school that is so well known. Though Radcliffe is fully integrated into Harvard College, unlike Barnard, Harvard does have other divisions that are not so integrated, including the “night school”.</p>