  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. 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 AdS_5xS^5 and Super YM
Conformal Field Theory in 4 dimensions. We conjecture that there is possibility
of breaking Supersymetry via sources of gravity generated in 4 dimensions by
exotic smooth structures on R^4 emerging in this context.
