overview

Implementable Set Theory

Instead of augmenting the already numerous attempts with one other attempt for founding the whole of Mathematics upon still another kind of Set Theory, quite a different strategy has been adopted in this chapter. Our purpose is to obtain a set theory which is just a theory of sets, that is: not suitable per se as a Foundation of Mathematics.
One thing that bothers us is: whether such a theory of sets can be implemented using existing - and future - computer hardware and software. Ultimately, it is our deepest wish that Implementable Set Theory shall be identified with virtually unlimited Computer Memory. In such a way that there are no bits and bytes left; our sets must be such that they are able to consume all memory of any digital computer (not yet) available.

  1. Set Implementations
  2. Axiom of Extension
  3. Axiom of Empty Set
  4. Hereditary Sets
  5. Number of the Beast
  6. Pairing and Union
  7. Complements and Powers
  8. Axiom of Foundation
  9. Ordered pairs
  10. Von Neumann successors
  11. Axiom of Infinity
  12. Specification Axiom
  13. Voronoi & Delaunay
  14. References
  15. Is it still possible for mathematicians
    to contribute to the theory of music?

Disclaimers

Anything free comes without referee :-(
My English may be better than your Dutch :-)