Theoria: An International Journal for Theory, History and Foundations of Science

Volume 18, Issue 2, Mayo 2003

Ignacio Jané
Pages 179-187

Remarks on Second-Order Consequence

Tarski’s definition of logical consequence can take different forms when implemented in second order languages, depending on what counts as a model. In the canonical, or standard, version, a model is just an ordinary structure and the (monadic) second-order variables are meant to range over all subsets of its domain. We discuss the dependence of canonical second-order consequence on set theory and raise doubts on the assumption that canonical consequence is a definite relation.