250082 VO Selected topics in mathematical logic (2014W)

The Philosphy and Mathematics of Set-Theoretic Truth

This will be a course devoted to the approach to Set-Theoretic Truth given by the Hyperuniverse Programme. I'll begin with a discussion of the Iterative Conception as well as the Potentialism vs. Actualism debate in our understanding of structure of the set-theoretic universe. Then after touching on various Multiverse Conceptions I'll focus in detail on the Hyperuniverse Programme: Mental pictures and Maximality, the Reduction to the Hyperuniverse, H-Axioms, the IMH and its variants, #-Generation and the Synthesis of Mathematical Criteria. The optimistic aim of the Programme is to discover new first-order consequences of the Maximality feature of the Universe of Sets which resolve fundamental problems in Set Theory such as the Continuum Problem.