A compactness property of Dedekind $\sigma$-complete f-rings
Wehrung, Friedrich
HAL, hal-00004655 / Harvested from HAL
Text on HAL
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 $K$.
Publié le : 1996-07-05
Classification:  Boolean models,  first-order languages,  $\sigma$-complete Boolean algebras,  atomic compactness,  Dedekind $\sigma$-complete f-rings,  03C90, 08A45, 06F05, 06F20, 54H99,  [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM] 
@article{hal-00004655,
     author = {Wehrung, Friedrich},
     title = {A compactness property of Dedekind $\sigma$-complete f-rings},
     journal = {HAL},
     volume = {1996},
     number = {0},
     year = {1996},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00004655}
}

Wehrung, Friedrich. A compactness property of Dedekind $\sigma$-complete f-rings. HAL, Tome 1996 (1996) no. 0, . http://gdmltest.u-ga.fr/item/hal-00004655/