Formal Definition
If λ is any ordinal, κ is λ-supercompact means that there exists an elementary embedding j from the universe V into a transitive inner model M with critical point κ, j(κ)>λ and
That is, M contains all of its λ-sequences. Then κ is supercompact means that it is λ-supercompact for all ordinals λ.
Alternatively, an uncountable cardinal κ is supercompact if for every A such that |A| ≥ κ there exists a normal measure over < κ.
< κ is defined as follows:
Read more about this topic: Supercompact Cardinal
Famous quotes containing the words formal and/or definition:
“The bed is now as public as the dinner table and governed by the same rules of formal confrontation.”
—Angela Carter (1940–1992)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)