This is an announcement for the paper "A Boolean algebra and a Banach space obtained by push-out iteration" by Antonio Aviles and Christina Brech. Abstract: Under the assumption that the continuum c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(N)/fin has under CH and in the aleph2-Cohen model. We prove a similar result in the category of Banach spaces. Archive classification: math.LO math.CT math.FA Mathematics Subject Classification: 06E05, 03E35, 03G05, 46B26, 54G05, 18A30 Submitted from: avileslo@um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.5051 or http://arXiv.org/abs/1012.5051