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Creative mathematics

Gödel's result can be interpreted as establishing the
creative nature of mathematics. It led to a hierarchy of unsolvable
problems and a second hierarchy of mathematical structures that
could solve these problems if we could *create* the required
mathematics. This chapter describes these hierarchies and suggests
boundary conditions for continued creative evolution of mathematics
and consciousness.

- Arithmetical Hierarchy
- Ordinal induction
- Axiom scheme of replacement
- Ordinal numbers
- Searching all possible paths
- Power set axiom
- Trees of trees
- Extending mathematics
- Is the cardinality of the reals 0 or ?
- A philosophy of mathematical truth

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