Computable Measure Theory

Representations of measurable sets in computable measure theory

This article is a fundamental study in computable measure theory. We use the framework of TTE, the representation approach, where computability on an abstract set X is defined by representing its elements with concrete “names”, possibly countably infinite, over some alphabet Σ. As a basic computability structure we consider a computable measure on a computable σ-algebra. We introduce and compar...

Computable Algebra, General Theory and Theory of Computable Fields(1)

Introduction. Abstract algebra is the product of a transition from such concrete systems as the ring of integers or the field of rational numbers to the corresponding, axiomatically defined, abstract systems. In the course of this abstraction process various properties of the concrete system are lost. The field of rational numbers, for example, possesses a natural topology, an ordering, and fur...

Pure Computable Model Theory

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Introduction History Notation and basic definitions Decidable theories, and computable and decidable models Effective completeness theorem Model completeness and decidability Omitting types and decidability Decidable prime models Computable saturated models and computably saturated models Decidable homogeneous models Vaught's theorem computabl...

Computable Model Theory

Computability theory formalizes the intuitive concepts of computation and information content. Pure computability studies these notions and how they relate to definability in arithmetic and set theory. Applied computability examines other areas of mathematics through the lens of effective processes. Tools from computability can be used to give precise definitions of concepts such as randomness....

Computable model theory