1. Reverse mathematics and well-ordering principles: A pilot study
- Author
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Afshari, Bahareh and Rathjen, Michael
- Subjects
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REVERSE mathematics , *MATHEMATICAL logic , *ELIMINATION (Mathematics) , *RECURSION theory , *COMBINATORICS , *MATHEMATICAL models - Abstract
Abstract: The larger project broached here is to look at the generally sentence “if is well-ordered then is well-ordered”, where 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 -models for a particular theory whose consistency can be proved by means of a cut elimination theorem in infinitary logic which crucially involves the function . To illustrate this theme, we prove in this paper that the statement “if is well-ordered then is well-ordered” is equivalent to . This was first proved by Marcone and Montalban [Alberto Marcone, Antonio Montalbán, The epsilon function for computability theorists, draft, 2007] using recursion-theoretic and combinatorial methods. The proof given here is principally proof-theoretic, the main techniques being Schütte’s method of proof search (deduction chains) [Kurt Schütte, Proof Theory, Springer-Verlag, Berlin, Heidelberg, 1977] and cut elimination for a (small) fragment of . [Copyright &y& Elsevier]
- Published
- 2009
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