Our goal is to construct mathematical operations that combine non-determinism measured from quantum randomness with computational determinism so that non-mechanistic behavior is preserved in the computation. Formally, some results about operations applied to computably enumerable (c.e.) and bi-immune sets are proven here, where the objective is for the operations to preserve bi-immunity. While developing rearrangement operations on the natural numbers, we discovered that the bi-immune rearrangements generate an uncountable subgroup of the  symmetric group on the natural numbers. The structure of this new subgroup  is unknown.
Our goal is to construct mathematical operations that combine indeterminism measured from quantum randomness with computational determinism so that non-mechanistic behavior is preserved in the computation. Formally, some results about operations applied to computably enumerable (c.e.) and bi-immune sets are proven here, where the operations preserve bi-immunity. While developing rearrangement operations on the natural numbers, we discovered that the bi-immune rearrangements generate an uncountable subgroup of the infinite symmetric group on the natural numbers. We show that this new subgroup contains the bounded symmetric group on the natural numbers, and consequently is highly transitive. The complete structure of this new subgroup and its subgroups generated by one or more bi-immune rearrangements is unknown.
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non-determinism
indeterminism
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objective is for the operations to
operations
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infinite
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The
We show that this new subgroup contains the bounded symmetric group on the natural numbers, and consequently is highly transitive. The complete
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and its subgroups generated by one or more bi-immune rearrangements