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H-fields and their Liouville extensions
Abstract. We introduce H-fields as ordered differential fields of a certain kind. Hardy fields extending ${\mathbb R}$, as well as the field of logarithmic-exponential series over ${\mathbb R}$ areExpand
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Generating the Greatest Common Divisor, and Limitations of Primitive Recursive Algorithms
AbstractThe greatest common divisor of two integers cannot be generated in a uniformly bounded number of steps from those integers using arithmetic operations. The proof uses an elementaryExpand
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Images of Additive Polynomials in 𝔽 q ((t)) Have the Optimal Approximation Property
Abstract We show that the set of values of an additive polynomial in several variables with arguments in a formal Laurent series field over a finite field has the optimal approximation property:Expand
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Definable Sets in Mann Pairs
Consider structures (Ω, k, Γ) where Ω is an algebraically closed field of characteristic zero, k is a subfield, and Γ is a subgroup of the multiplicative group of Ω. Certain pairs (k, Γ) have beenExpand
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On the elementary theory of rings of Witt vectors with a multiplicative set of representatives for the residue field
Abstract:We indicate a complete set of elementary invariants for the ring of Witt vectors over a perfect field of prime characteristic, where this ring is equipped with its unique multiplicative setExpand