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Reverse mathematics and well-ordering principles: A pilot study
- Source :
-
Annals of Pure & Applied Logic . Sep2009, Vol. 160 Issue 3, p231-237. 7p. - Publication Year :
- 2009
-
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]
Details
- Language :
- English
- ISSN :
- 01680072
- Volume :
- 160
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Annals of Pure & Applied Logic
- Publication Type :
- Academic Journal
- Accession number :
- 44038428
- Full Text :
- https://doi.org/10.1016/j.apal.2009.01.001