We settle a number of questions concerning definability in first order logic with an extra predicate symbol ranging over semi-linear sets. We give new results both on the positive and negative side: ...

A semantical definition of abstract logics is given. It is shown that the Craig interpolation property implies the Beth definability property, and that the Souslin-Kleene interpolation property ...

Set theory remains the fulcrum of modern mathematical foundations, providing the language and axiomatic structure upon which much of mathematics is built. Predominantly formulated through the ...