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.
- Set Implementations
- Axiom of Extension
- Axiom of Empty Set
- Hereditary Sets
- Number of the Beast
- Pairing and Union
- Complements and Powers
- Axiom of Foundation
- Ordered pairs
- Von Neumann successors
- Axiom of Infinity
- Specification Axiom
- Voronoi & Delaunay
- References
- 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 :-)