Computably Categorical Fields via Fermat's Last Theorem
Russell Miller, Hans Schoutens
TL;DR
This paper constructs a computable, computably categorical field with infinite transcendence degree over rationals, utilizing Fermat polynomials and algebraic geometry, and demonstrates it has an intrinsically computable transcendence basis.
Contribution
It introduces a novel construction of a computably categorical field with infinite transcendence degree using Fermat polynomials, and proves the basis is intrinsically computable.
Findings
Constructed a computable, computably categorical field of infinite transcendence degree.
Proved the field has an intrinsically computable transcendence basis.
Abstract
We construct a computable, computably categorical field of infinite transcendence degree over the rational numbers, using the Fermat polynomials and assorted results from algebraic geometry. We also show that this field has an intrinsically computable (infinite) transcendence basis.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Advanced Topology and Set Theory · Mathematical Dynamics and Fractals