**Abstract.** This article is one of a series explaining the nature of mathematical undecidability discovered within quantum theory. Crucially, a formula’s undecidability certifies its indeterminacy and vice versa. This paper describes the algebraic environment in which the undecidability and indeterminacy originate; provides proof of their existence; and demonstrates the role these play in a three-valued logic which is free to permeate mathematical physics via this algebra.

The radical idea applied in this research is taken from very well-known results in mathematical logic. All scalars engage in the arithmetic of scalars by way of a single algebra. But in terms of validity, these scalars partition into sets which are logically distinct: those with valid existence with respect to this algebra, and those with indeterminate existence. Failure of mathematical physics to notice this distinction is the reason why quantum theory is logically at odds with quantum experiments.

http://www.vixra.org/pdf/1101.0045v3.pdf

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