Section: New Results

Inductive reasoning

• Participants: Isabelle Gnaedig, Sofien Ben Ayed

We are interested in quantifying the power of axiomatic theories. For this purpose, induction is a key concept. We have investigated the different validity proofs of inductive reasoning, the equivalence of induction with the well-ordered principle and well-foundedness, the differences between first and second order forms of the induction principle, and the notion of $\omega$-consistency, qualifying theories interpreting arithmetic for which proving a property for each value of standard integers does not imply that the property is always true. We have also studied the importance of the axiom of choice for induction, and analysed a recent interpretation of induction by Hardin and Taylor through the hat problem [22].