Geodesic
Independent Sets of Axioms In Lκα
Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 219-223

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A set of sentences T is called independent if for every . It is countably independent if every countable subset is independent. In flnitary first order logic, L ωω, the two notions coincide because of compactness. This is not the case for infinitary logic. 
Caicedo, Xavier. Independent Sets of Axioms In Lκα. Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 219-223. doi: 10.4153/CMB-1981-034-x
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     author = {Caicedo, Xavier},
     title = {Independent {Sets} of {Axioms} {In} {L\ensuremath{\kappa}\ensuremath{\alpha}}},
     journal = {Canadian mathematical bulletin},
     pages = {219--223},
     year = {1981},
     volume = {24},
     number = {2},
     doi = {10.4153/CMB-1981-034-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-034-x/}
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