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@ARTICLE{,
    author = {C{\'{u}}th, Marek},
     title = {Separable determination in Banach spaces},
   journal = {Fundamenta Mathematicae},
    volume = {243},
    number = {1},
      year = {2018},
     pages = {9-27},
       doi = {10.4064/fm480-11-2017},
  abstract = {We study a relation between three different formulations of theorems on separable determination: one using the concept of rich families, another via the concept of suitable models, and a third, new one, suggested in this paper, using the notion of ω-monotone mappings. In particular, we show that in Banach spaces all those formulations are in a sense equivalent, and we give a positive answer to two questions of O. Kalenda and the author. Our results enable us to obtain new statements concerning separable determination of σ-porosity (and of similar notions) in the language of rich families; thus, without using any terminology from logic or set theory.

Moreover, we prove that in Asplund spaces, generalized lushness is separably determined.}
}