Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo
Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics (going back from the theorems to the axioms). Reverse mathematics makes use of subsystems of second order arithmetic ( a formal theory of the natural numbers and sets of natural numbers). These ”base” systems are too weak to prove most of the interesting theorems in mathematics, but powerful enough to state these theorems and maybe prove one from another. We describe five basic subsystems of second order arithmetic (Big Five) that occur frequently in reverse mathematics. In particular, we will focus on ACA0 and weaker systems (mathematics that can be done with sets from the arithmetic hierarchy) and compare their strength. Also we point out facts that explain the close connection between reverse mathematics and computability theory.
Note: This is our first talk as we begin our new topic of Reverse Mathematics. We will be working through Hirschfeldt’s ”Slicing the Truth”.
MC 5413