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.
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.
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