Breakdown of Bell's theorem for certain objective local parameter spaces.

We show that the known proofs of Bell's inequalities contain algebraic manipulations that are not appropriate within the syntax of Kolmogorov's axioms for probability theory without detailed justification. Such justification can be achieved by a variant of the techniques used in Bell-type proofs but only for a subclass of objective local parameter spaces. It cannot be achieved for an extended parameter space that is still objective local and that includes instrument parameters correlated by both time and setting dependencies.