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PRIMITIVE RECURSIVE DECIDABILITY FOR THE RING OF INTEGERS OF THE COMPOSITUM OF ALL SYMMETRIC EXTENSIONS OF ℚ

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Abstract Let ℚsymm be the compositum of all symmetric extensions of ℚ, i.e., the finite Galois extensions with Galois group isomorphic to Sn for some positive integer n, and let… Click to show full abstract

Abstract Let ℚsymm be the compositum of all symmetric extensions of ℚ, i.e., the finite Galois extensions with Galois group isomorphic to Sn for some positive integer n, and let ℤsymm be the ring of integers inside ℚsymm. Then, TH(ℤsymm) is primitive recursively decidable.

Keywords: compositum symmetric; ring integers; symmetric extensions; recursive decidability; decidability ring; primitive recursive

Journal Title: Glasgow Mathematical Journal
Year Published: 2020

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