Nice infinitary logics

by Shelah. [Sh:797]
J American Math Soc, 2012
We deal with soft model theory of infinitary logics. We find a logic between {mathbb L}_{infty, aleph_0} and L_{infty, infty} which has some striking properties. First, it has interpolations (it was known that each of those logics fail interpolation though

the pair has). Second, well ordering is not characterized in a strong way. Third, it can be characterized as the maximal such nice logic (in fact, is the maximal logic stronger than L_{infty, aleph_0} and which satisfies ``well ordering is not characterized in a strong way'').


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