### 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 thoughthe 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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