Jeffry Hirst - Some conservation results for higher order reverse mathematics

This lecture was part of the Workshop on "Reverse Mathematics: New Paradigms" held at the ESI August 4 - 8, 2025. This talk examines conservation results for some weak systems of higher order reverse mathematics over second order arithmetic. Results of this sort can allow the use of expressive higher order axioms to prove results in traditional subsystems. Older results will be surveyed, with the inclusion of some newer and preliminary work, plus open questions.