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Easton's theorem for the tree property below aleph_omega (1907.03737v1)
Published 8 Jul 2019 in math.LO
Abstract: Starting with infinitely many supercompact cardinals, we show that the tree property at every cardinal $\aleph_n$, $1 < n <\omega$, is consistent with an arbitrary continuum function below $\aleph_\omega$ which satisfies $2{\aleph_n} > \aleph_{n+1}$, $n<\omega$. Thus the tree property has no provable effect on the continuum function below $\aleph_\omega$ except for the restriction that the tree property at $\kappa{++}$ implies $2\kappa>\kappa+$ for every infinite $\kappa$.