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Reverse Mathematics and Well-ordering Principles
Pure Mathematics
University of Leeds
4pm Tuesday 13th of January, 2009
Room 4.31/4.33, Informatics Forum
Abstract
The larger project broached here is to look at the generally Π12
sentence "if X is well ordered then f(X) is well ordered", where f is
a standard proof theoretic function from ordinals to ordinals. It has
turned out that a statement of this form is often equivalent to the
existence of countable coded omega-models for a particular theory Tf
whose consistency can be proved by means of a cut elimination theorem
in infinitary logic which crucially involves the function f. To
illustrate this theme, I show how the statement "if X is well ordered
then εX is well ordered" is equivalent to ACA0+. This was
first proved by Marcone and Montalban using recursion-theoretic and
combinatorial methods. The proof given in this talk will be
principally proof-theoretic, the main techniques being Schütte's
method of proof search (deduction chains) and cut elimination for a
variant of ACA∞.
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