The Center for the Advancement of Logic, its Philosophy, History and Applications presents
"On Set-Theoretic and Transfinite Analogues of Epistemic Arithmetic and Flagg Consistency"
with Benjamin G. Rin, Graduate Student, Department of Logic & Philosophy of Science, UC Irvine
Wednesday, January 29, 2014
Social Science Tower, Room 777
In the early '80s, Shapiro proposed that we could understand and fruitfully analyze the pre-theoretic notion of computability within the framework of a modal version of arithmetic (essentially PA + S4) known as epistemic arithmetic (EA). Soon after, Flagg produced crucial evidence for Shapiro's proposal in a well-known article that proved the consistency of Church's Thesis with EA. (Here he used an epistemic version of Church's Thesis, called ECT.) In this talk, Rin will look at the possibility of extending Flagg's result to a richer base theory, by replacing Peano arithmetic with Kripke-Platek set theory and, in turn, substituting ECT with an infinitary analogue-- one that centers on Hamkins-Lewis infinite time Turing machines or even ordinal Turing machines in place of ordinary Turing machines. Doing this should clarify the limits of Flagg's contribution, by informing us to what extent, if any, it depends on the built-in assumptions of finiteness inherent in traditional Turing computability.
For further information, please contact Patty Jones, firstname.lastname@example.org or 949-824-1520.