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.
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 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 infinite symmetric group (Sym(\mathbb{N on the natural numbers \mathbb{N We show that the bi-immune symmetric group contains the finitary symmetric group on the natural numbers, and consequently is highly transitive. Furthermore, the bi-immune symmetric group is dense in Sym(\mathbb{N The complete structure of the bi-immune symmetric group and its subgroups generated by one or more bi-immune rearrangements is unknown.
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operations
objective is for the operations to
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(Sym(\mathbb{N
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\mathbb{N
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this new subgroup contains the bounded
the bi-immune symmetric group contains the finitary
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Furthermore, the bi-immune symmetric group is dense in Sym(\mathbb{N
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this new subgroup
the bi-immune symmetric group