In Badiou's lecture on 'The Event as Creative Novelty 2009' (here: https://www.youtube.com/watch?v=ZekT_HQmYo8 and here: https://dingpolitik.wordpress.com/2013/07/22/alain-badiou-the-three-fundamental-logics-of-negation-hyper-transcription/ ) where even Zizek makes a brief cameo in the Q&As, Badiou states roughly that:

[T]he logic of an event is neither reducible to pure being or to the laws of existence. This is why there are three logics and not only two; it is because there are three types of being.

Am I to take away that like Escher's 'Waterfall' drawing that the 3 logics (as the 3 logics of being) are occurring simultaneously and dialectically (as the ec-static subject, wherever it is not and whoever it is not), and thus that Badiou's Being is associated with Zizek's Nothing/Void (and Lacan's Real?), Badiou's Existence is associated with Zizek's Something (and Lacan's Symbolic?), and Badiou's Event is associated with Zizek's Less Than Nothing (and Lacan's Imaginary?), aka Den, aka Objet A -- with the equation that Something is more than Nothing, Den is more than Something, and Den is Less than Nothing?

And if this is the case, can you explicate Badiou's 'forcing' (of an Event whose Subject is the newly uptaken endeavor to the fidelity of that very Event, to uphold its briefly appearing but indefinitely reassessed implications of its Truth) in terms of how Zizek talks about the Objet A, fantasy, and traversing the fantasy?

(Absolute Recoil has some stuff on this very topic too, here and the surrounding pages)