An Omitting Types Theorem for positive bounded formulas in normed spaces Original Research Article

Inspired by a construction of the Tsirelson space (Lindenstrauss and Tzafriri, Classical Banach Spaces, Springer, Berlin, 1977), we prove a general theorem for omitting countably many positive formulas in normed spaces. This theorem can be used in functional analysis as a tool to guarantee the existence of complicated normed spaces without having to construct them. The proof of this result is based on the notion of approximate truth and on a study of the relationship between approximate truth and convergence in normed spaces. We illustrate the power of this result with an application to functional analysis.