Abstract
Since Cohen forcing is countable, it satisfies ccc, hence, Cohen forcing is proper. Furthermore, since forcing notions with the Laver property do not add Cohen reals, Cohen forcing obviously does not have the Laver property.
Not so obvious are the facts that Cohen forcing adds unbounded and splitting, but no dominating reals.
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Halbeisen, L.J. (2017). Cohen Forcing Revisited. In: Combinatorial Set Theory. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-60231-8_22
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