This is an announcement for the paper "Pre-compact families of finite sets of integers and weakly null sequences in Banach spaces" by Jordi Lopez Abad and S. Todorcevic. Abstract: We provide a somewhat general framework for studying weakly null sequences in Banach spaces using Ramsey theory of families of finite subsets of integers Archive classification: Functional Analysis; Logic Mathematics Subject Classification: MSC: 05d10, 46b20 The source file(s), lop-tod.tex: 145237 bytes, is(are) stored in gzipped form as 0510407.gz with size 41kb. The corresponding postcript file has gzipped size 136kb. Submitted from: abad@logique.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0510407 or http://arXiv.org/abs/math.FA/0510407 or by email in unzipped form by transmitting an empty message with subject line uget 0510407 or in gzipped form by using subject line get 0510407 to: math@arXiv.org.