Infinite time computable model theory
  We introduce infinite time computable model theory, the computable model theory arising with infinite time Turing machines, which provide infinitary notions of computability for structures built on the reals R. Much of the finite time theory generalizes to the infinite time context, but several fundamental questions, including the infinite time computable analogue of the Completeness Theorem, turn out to be independent of ZFC. 
Joel David Hamkins (The City University of New York), Russell Miller   (The City University of New York), Daniel Seabold (Ho...