A Boolean algebra and a Banach space obtained by push-out iteration

TL;DR

This paper constructs unique Boolean algebra and Banach space structures of size c using push-out iteration, mirroring properties known under CH and in the aleph2-Cohen model, under the assumption that c is a regular cardinal.

Contribution

It introduces a method to obtain unique Boolean algebra and Banach space structures of size c via push-out iteration, extending known models under specific set-theoretic assumptions.

Findings

Existence and uniqueness of Boolean algebra B of size c

Existence and uniqueness of Banach space with similar properties

Results depend on c being a regular cardinal

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.