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arXiv · 2412.20432

Relative Constructibility via Generalised Sequential Algorithms

Desmond Lau
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Abstract

We modify Gurevich's definition of sequential algorithms, so that it becomes amenable to computation with arbitrarily large sets on a sufficiently intuitive level. As a result, two classes of abstract algorithms are obtained, namely generalised sequential algorithms (GSeqAs) and generalised sequential algorithms with parameters (GSeqAPs). We derive from each class a relative computability relation on sets which is analogous to the Turing reducibility relation on reals. We then prove that the relative computability relation derived from GSeqAPs is equivalent to the relative constructibility relation in set theory.

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Desmond Lau. 2024-12-29. Relative Constructibility via Generalised Sequential Algorithms. https://arxiv.org/abs/2412.20432

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