In the introduction to his seminar L’INFINI: ARISTOTE, SPINOZA, HEGEL (1984-1985) Badiou lists eight fundamental theses concerning the concepts of the One and the Infinite. Three are contained in BEING AND EVENT (1988) :
“1. The One is not, being is given only in the form of the multiple.
2. A situation, thought as multiple, is in general infinite.
3. Every truth, considered in its being-multiple, is infinite”.
Five more have been added in his subsequent works, Logics of Worlds (2006) and The Immanence of Truths (forthcoming):
“4. Every world is a multiple measured by an inaccessible infinite cardinal.
5. In every world, there is one and only one element which is the inexistent of this world.
6. The finite does not exist. It results from the combined action of two infinites of different types.
7. Under the action of the infinity of truth, every finite production is divided into the work and the waste product.
8. Finitude is the essence of all oppression, and its overcoming supposes an infinite that is new to the regard of those who structure the world considered”.