Unfolding Schematic Formal Systems
Solomon Feferman, Depts. of Mathematics and Philosophy,
Stanford University
Abstract:
The unfolding of schematic formal systems is a novel concept which weds:
(i) functional (least fixed point) schemata for recursion over arbitrary
structures, to (ii) schematic formal systems S considered in a wider, more
open-ended sense than is customary in current metamathematics. The
concept of unfolding is used to answer the following general question:
*What operations, predicates and principles concerning them are implicit
in the acceptance of a given schematic system S?*
I will report on joint work with Thomas Strahm characterizing the
notion of unfolding for non-finitist arithmetic, and then will explain
open problems for this concept ranging from feasible and
finitist arithmetic to higher set theory.
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