We designed \(\small\mathbb M\)ATh as a foundation of mathematics which is compatible with practical usage in German undergraduate university mathematics. In particular, we have tried to:
- maximize compatibility with traditional notation and concepts,
- use sets in a naive but rigorous and consistent way,
- avoid the laborious construction of relations and functions from sets,
- integrate a natural handling of mathematical models and theories,
- enable computer support without requiring it.
To achieve that, various aspects have to be addressed:
- generation rules for objects and statements
- axioms and inference rules
- partially determined contexts in models and theories
- handling of undefinedness
- introduction of new notation