Abstract
It is stated that if a Boolean family W of valuation rings of a field F satisfies the block approximation property (BAP) and a global analog of the Hensel-Rychlick property (THR), in which case 〈F, W〉 is called an RC*-field, then F is regularly closed with respect to the family W (The-orem 1). It is proved that every pair 〈F, W〉, where W is a weakly Boolean family of valuation rings of a field F, is embedded in the RC*-field 〈F0, W0〉 in such a manner that R0 ↦ R0 ∩ F, R0 ∈ W0 is a continuous map, W0 is homeomorphic over W to a given Boolean space, and R0 is a superstructure of R0 ∩ F for every R0 ∈ W0 (Theorem 2).
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References
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Additional information
Translated fromAlgebra i Logika, Vol. 33, No. 4, pp. 367–386, July-August, 1994.
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Ershov, Y.L. RC *-fields. Algebr Logic 33, 205–215 (1994). https://doi.org/10.1007/BF00750847
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DOI: https://doi.org/10.1007/BF00750847