Scott isomorphism theorem
= Scott isomorphism theorem
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= Scott's isomorphism theorem
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{synonym}
Every countable structure in a countable <first-order language> has a <Scott sentence>. Hence countable structures satisfying the same sentences of <countable infinitary logic> are <isomorphic>. The proof uses <Scott formulas>, stabilization on the countable set of finite <tuples>, and the <back-and-forth method>.