Set Theoretical Forcing in Quantum Mechanics and AdS/CFT Correspondence

We show unexpected connection of Set Theoretical Forcing with Quantum Mechanical lattice of projections over some separable Hilbert space. The basic ingredient of the construction is the rule of indistinguishability of Standard and some Nonstandard models of Peano Arithmetic. The ingeneric reals introduced by M. Ozawa will correspond to simultaneous measurement of incompatible observables. We also discuss some results concerning model theoretical analysis of Small Exotic Smooth Structures on topological 4-space ⁴. Forcing appears rather naturally in this context and the rule of indistinguishability is crucial again. As an unexpected application we are able to approach Maldacena Conjecture on AdS/CFT correspondence in the case of AdS₅ × S⁵ and Super YM Conformal Field Theory in four dimensions. We conjecture that there is possibility of breaking Supersymetry via sources of gravity generated in four dimensions by exotic smooth structures on ⁴ emerging in this context.