σ-Porosity is separably determined

We prove a separable reduction theorem for σ-porosity of Suslin sets. In particular, if A is a Suslin subset in a Banach space X, then each separable subspace of X can be enlarged to a separable subspace V such that A is σ-porous in X if and only if A∩V is σ-porous in V. Such a result is proved for several types of σ-porosity. The proof is done using the method of elementary submodels, hence the results can be combined with other separable reduction theorems. As an application we extend a theorem of L. Zají?ek on differentiability of Lipschitz functions on separable Asplund spaces to the nonseparable setting.