FOM: transfinite progressions etc.

[Neil Tennant]

Could anyone please refer me to recent, state-of-the-art presentations of
known results and open problems in the following areas:

1. Transfinite recursive progressions of arithmetical theories.
2. Ditto, but starting with HA and using only intuitionistic logic for
closure at every stage.
3. HA* (HA with axiom schemata of transfinite induction for recursive
well-orderings).

I am looking for technical results relevant to the philosophical problem
of assessing the extent to which first-order Th(N) depends on the specific
contribution of *classical* logic, rather than on the contribution of a
constructive grasp of the natural numbers. This is perforce vague, but
I trust that members of this list will get my drift.

___________________________________________________________________
Neil W. Tennant
Professor of Philosophy and Adjunct Professor of Cognitive Science

http://www.cohums.ohio-state.edu/philo/people/tennant.html

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