Completions of Convexly Ordered Valuation Rings

Mathematical Logic Quarterly 40 (3):318-330 (1994)
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Abstract

We prove that every convexly ordered valuation ring has a unique completion as a uniform space, which furthermore is a convexly ordered valuation ring. In addition, we give a model theoretic characterisation of complete convexly ordered valuation rings, and give a necessary and sufficient condition for the completion of a convexly ordered valuation ring to be a real closed ring

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10.1002/malq.19940400303

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Hilbert's 17th Problem for Real Closed Rings.Larry Mathews - 1994 - Mathematical Logic Quarterly 40 (4):445-454.

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