TY - GEN UR - http://lib.ugent.be/catalog/pug01:1247669 ID - pug01:1247669 LA - eng TI - Reverse mathematics and well-ordering principles PY - 2011 SN - 9781848162778 PB - Singapore AU - Rathjen, Michael AU - Weiermann, Andreas WE01 802000038735 0000-0002-5561-5323 AU - Cooper, S Barry editor AU - Sorbi, Andrea editor AB - The paper is concerned with generally Pi^1_2 sentences of the form '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 T_f 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, we shall focus on the well-known psi-function which figures prominently in so-called predicative proof theory. However, the approach taken here lends itself to generalization in that the techniques we employ can be applied to many other proof-theoretic functions associated with cut elimination theorems. In this paper we show that the statement 'if X is well ordered then 'X0 is well ordered' is equivalent to ATR0. This was first proved by Friedman, Montalban and Weiermann [7] using recursion-theoretic and combinatorial methods. The proof given here is proof-theoretic, the main techniques being Schuette's method of proof search (deduction chains) [13], generalized to omega logic, and cut elimination for infinitary ramified analysis. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 1247669 | ||
005 | 20180813140802.0 | ||
008 | 110530s2011------------------------eng-- | ||
020 | a 9781848162778 | ||
024 | a 1854/LU-1247669 2 handle | ||
040 | a UGent | ||
245 | a Reverse mathematics and well-ordering principles | ||
260 | a Singapore, Singapore b World Scientific c 2011 | ||
520 | a The paper is concerned with generally Pi^1_2 sentences of the form '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 T_f 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, we shall focus on the well-known psi-function which figures prominently in so-called predicative proof theory. However, the approach taken here lends itself to generalization in that the techniques we employ can be applied to many other proof-theoretic functions associated with cut elimination theorems. In this paper we show that the statement 'if X is well ordered then 'X0 is well ordered' is equivalent to ATR0. This was first proved by Friedman, Montalban and Weiermann [7] using recursion-theoretic and combinatorial methods. The proof given here is proof-theoretic, the main techniques being Schuette's method of proof search (deduction chains) [13], generalized to omega logic, and cut elimination for infinitary ramified analysis. | ||
598 | a C1 | ||
100 | a Rathjen, Michael | ||
700 | a Weiermann, Andreas u WE01 0 802000038735 0 0000-0002-5561-5323 9 F8586FE6-F0ED-11E1-A9DE-61C894A0A6B4 | ||
700 | a Cooper, S Barry e editor | ||
700 | a Sorbi, Andrea e editor | ||
650 | a Mathematics and Statistics | ||
653 | a ATR0 | ||
653 | a countable | ||
653 | a coded omega-model | ||
653 | a reverse mathematics | ||
653 | a Schütte deduction chains | ||
653 | a well ordering principles | ||
773 | t Computability in Europe 2007 (CiE 2007) : Computation and logic in the real world g Computability in context : computation and logic in the real world. 2011. World Scientific. p.351-370 q :<351 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/1247669/file/1247689 z [open] y RevWO2.pdf | ||
920 | a confcontrib | ||
Z30 | x WE 1 WE01 | ||
922 | a UGENT-WE |
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