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Asaf Karagila
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Are there recursive sets $X$ with Property A that contain infinitely many incompressible strings?

Let us say a set $X$ satisfies Property A if$$\liminf_{n \to \infty} {{\left|X^{\le n}\right|}\over n} = 0.$$Are there recursive sets $X$ satisfying Property A that contain infinitely many incompressible strings?