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The Winesburg, Ohio collection by Sherwood Anderson, obviously Chekhov, Nine Stories by J.D. Salinger, Signs and Symbols by Nabokov, Lost in the Funhouse by John Barth, and That Evening Sun by Faulkner, even though Faulkner has a lot of very nice ones.
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Borges Borges Borges. I am in the cult. Flannery O'Connor? Raymond Carver is highly recommended by some though I don't see it. Bolano's stories perhaps although it's better to read 2666 and Savage Detectives, they're all in there. Arthur Conan Doyle, Chesterton: good, fun reads.