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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