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If at Deligne completeness theorem we read
When in the early 70s the connection between topos theory and logic became manifest William Lawvere (1975) pointed out that the theorem may be viewed as a variant of the classical Gödel-Henkin completeness theorem for first-order logic,
what could be said in a similar vein at it’s $(\infty, 1)$-generalization Deligne-Lurie completeness theorem? What would play the role of coherent logic?
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