# Research Interests

My primary research is in minimal logic. Minimal logic is a generalisation of
intuitionistic logic in which *ex falso quodlibet* is not assumed. This leaves
no axioms regarding negation or absurdity. In fact, absurdity is just a
proposition, which may or may not hold. For this reason, minimal logic may be
thought of as the positive fragment of logic.

## Minimal Reverse mathematics

Reverse mathematics over minimal logic - classification and separation of classical tautologies which are not minimally derivable. Specifically, I examine principles in predicate logic. These include the ‘omniscience principles’ like LPO), and related principles like the drinker paradox.

## Minimal analysis

Analysis over minimal logic.

- Required changes to the Peano axioms in order to obtain a definition of the rational numbers in minimal logic.
- Modifications of proofs in Bishop’s constructive analysis to remove reliance on EFQ and disjunctive syllogism.
- Non-standard analysis over minimal logic.

# Contact

Direct your spam to rick@lsw.nz. Of course, my name is not Rick, so if you want to contact me use Louis instead.