Reflection theorems for cardinal functions

This paper is a systematic study of reflection theorems for cardinal functions. There are four sections: theory of reflection; reflection theorems for c, e, s, hd, hL, L, d, and nw; reflection theorems for χ, t, ψ, and psw (assuming compactness); reflection theorems for w, pw, and πw. This last section includes a standard (i.e., without elementary submodels) proof of Dowʹs remarkable theorem that every countably compact space that is not metrizable has a subspace of cardinality at most ω1 that is not metrizable.