English

Omitting uncountable types, and the strength of $[0,1]$-valued logics

Logic 2012-02-28 v1

Abstract

We study [0,1][0,1]-valued logics that are closed under the {\L}ukasiewicz-Pavelka connectives; our primary examples are the the continuous logic framework of Ben Yaacov and Usvyatsov \cite{Ben-Yaacov-Usvyatsov:2010} and the {\L}ukasziewicz-Pavelka logic itself. The main result of the paper is a characterization of these logics in terms of a model-theoretic property, namely, an extension of the omitting types theorem to uncountable languages.

Keywords

Cite

@article{arxiv.1202.5981,
  title  = {Omitting uncountable types, and the strength of $[0,1]$-valued logics},
  author = {Xavier Caicedo and José Iovino},
  journal= {arXiv preprint arXiv:1202.5981},
  year   = {2012}
}