Mathematical Problems from Applied Logic II

On Two Models of Provability: Provability Logic, Logic of Proofs.- Directions for Computability Theory Beyond Pure Mathematical: Motivations, Directions, Progress So Far And How One Might Go From Here.- Computability and Computable Models: Preliminaries, Bounds for Computable Models, Structure Complexity of Computable Models, Isomorphism Problem, Classes of Computable Models and Index Sets.- First-order Logic Foundation of Relativity Theories: Introduction (Logic and Spacetime Geometry), More Concrete Introduction (Foundation of Spacetime), Intriguing Features of GR Spacetimes (Challenges for the Logician), A FOL Axiom System of SR Extended with Accelerated Observers, One Step toward GR (Effect of Gravitation on Clocks), Questions, Suggestions for Future Research.- Beyond Hybrid Systems: Digital Programs, Continuous Plants and Controllers, Hybrid Systems, Discretization, Continualization, Methodology.- Region-Based Theory of Space: Algebras of Regions, Representation Theory, and Logics: Historical Excursion in the Region-Based Theory of Space, Algebras of Regions, Models, and Representation Theory, Region-Based Propositional Modal Logics of Space.