- Background
- What's wrong with first order set theory?
- Ideas on possible improvements.
- Methods for developing new classical foundation system
- Putting the ideas into practice.

The systems described here have been motivated by the desire to improve on classical first order set theory as an underlying logical system for use in applications in Computer Science, particularly in formal specfications.

- Use of operators not in the domain of discourse.
- Special treatment of Boolean values and operators.
- Founded on sets rather than functions.
- Lack of large scale structuring mechanisms.

- The system will be essentially classical, and easily shown to be equivalent in proof theoretic strength to ZFC.
- The system will have a minimal set of operators which are not in the domain of discourse, and will not require extension of this set of operators to suit applications.
- The system will be type-free, and will be suitable for semantic foundations for typed systems.
- The system will support structuring mechanisms which at a minimum will permit the use of local names without disadvantage relative to the use of global names.
- The system will provide a satisfactory notion of polymorphism.

- The Theory of Pure Functions
- The Theory of Pure Polymorphic Functions
- The Theory of Structured Polymorphic Functions

- The definition of the semantic domains in turn
- The definition of a suitable set of operators over these domains.
- The establishment of key properties of these operators.