Article Dans Une Revue Algebra Universalis Année : 1996

A compactness property of Dedekind $\sigma$-complete f-rings

Résumé

We prove that Dedekind $\sigma$-complete f-rings are boundedly countably atomic compact in the language $(+,-,\cdot,\wedge,\vee,\leq)$. This means that whenever $\Gamma$ is a countable set of atomic formulas with parameters from some Dedekind $\sigma$-complete f-ring $A$ every finite subsystem of which admits a solution in some fixed product $K$ of bounded closed intervals of $A$, then $\Gamma$ admits a solution in $K$.

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Dates et versions

hal-00004655 , version 1 (08-04-2005)

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Friedrich Wehrung. A compactness property of Dedekind $\sigma$-complete f-rings. Algebra Universalis, 1996, 36 (4), pp.511-522. ⟨10.1007/BF01233921⟩. ⟨hal-00004655⟩
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