l -Groups C in continuous logic

Archive for Mathematical Logic 57 (3-4):239-272 (2018)
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Abstract

In the context of continuous logic, this paper axiomatizes both the class \ of lattice-ordered groups isomorphic to C for X compact and the subclass \ of structures existentially closed in \; shows that the theory of \ is \-categorical and admits elimination of quantifiers; establishes a Nullstellensatz for \ and \; shows that \\in \mathcal {C}\) has a prime-model extension in \ just in case X is Boolean; and proves that in a sense relevant to continuous logic, positive formulas admit in \ elimination of quantifiers to positive formulas.

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10.1007/s00153-017-0566-3

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Citations of this work

Preservation properties for products and sums of metric structures.Mary Leah Karker - 2023 - Archive for Mathematical Logic 62 (3):427-469.

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References found in this work

The Theory of Ultrafilters.W. W. Comfort & S. Negrepontis - 1976 - Journal of Symbolic Logic 41 (4):782-783.

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