LLC Seminar: Quasi-Inductive Definitions
Philip Welch (University of Bristol)
9th June 2022 | Palazzo Nuovo Turin
Published: Wednesday, June 8, 2022
Quasi-Inductive Definitions
Such definitions extend the well-researched theory of monotone inductive definitions by allowing non-monotone processes that are structured by liminf rules at limits rather than simple unions. Much of the Moschovakian theory of induction over abstract structures can be performed in this context, resulting in certain Spector classes of sets. Whereas the theory of inductive definitions leads to the idea of the least admissible set over a structure A, here one constructs the least 'strongly Sigma_2-admissible set' over A. Examples of such quasi-inductions are not legion, but seem to have been more of interest to philosophers in theories of truth, and in infinite time Turing machines - machines which are essentially Turing machines, but allowed to compute into the transfinite.
Such definitions extend the well-researched theory of monotone inductive definitions by allowing non-monotone processes that are structured by liminf rules at limits rather than simple unions. Much of the Moschovakian theory of induction over abstract structures can be performed in this context, resulting in certain Spector classes of sets. Whereas the theory of inductive definitions leads to the idea of the least admissible set over a structure A, here one constructs the least 'strongly Sigma_2-admissible set' over A. Examples of such quasi-inductions are not legion, but seem to have been more of interest to philosophers in theories of truth, and in infinite time Turing machines - machines which are essentially Turing machines, but allowed to compute into the transfinite.
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