To rephrase the question, what is the relationship between:

• The univocity of Being (qua pure inconsistent multiplicity)
• The multiplicity of situations
• The integrity of any situation, qua consistent multiplicity “counted as one”
• The plurality of worlds (and of logics of worlds)
• The logical consistency of a world
• The “experimental” political performative assertion that this world is one, and not two
• The “one becomes two” of political antagonism

In particular: might one be misled here by the homonymy between “world” (logically consistent structuring of a situation - any situation, one amongst others) and “World” (shared existential situation of all living political agents, here and now)?

UPDATE: Jean-Luc Nancy, in Being Singular Plural:

The unity of a world is not one: it is made of a diversity, and even disparity and opposition. It is in fact, which is to say that is does not add or subtract anything. The unity of a world is nothing other than its diversity, and this, in turn, is a diversity of worlds. A world is a multiplicity of worlds; the world is a multiplicity of worlds, and its unity is the mutual sharing and exposition of all its worlds - within this world.

The diversity of worlds is univocally diverse; there is only one diversity. For Nancy, the “mutual sharing and exposition” of worlds is due to their givenness: every world is a donation of the same multiplicity. The theme of givenness is almost entirely absent in Badiou: there are operations which compose multiplicities, but no sense in which these operations are the apportioning of some endlessly self-giving reserve of being (the Virtual, for example). Chaos is no more primordial than order.