TY - JOUR
T1 - The Galvin-Prikry theorem and set existen axioms
AU - Tanaka, Kazuyuki
PY - 1989/3/28
Y1 - 1989/3/28
N2 - H. Friedman observed the following phenomenon (or the 'theme' of Reverse Mathe in many branches of ordinary mathematics: When the theorem is proved from the right the axioms can be proved from the theorem. In this paper, we give an instance that the of Reverse Mathematics does not apply to the lightface statements, by demonstrating statement that all Σ11 partitions are Ramsey is deducible over the system ATR0 from the of Σ11 monotone inductive definition, but the reversal is not deducible over ATR0.
AB - H. Friedman observed the following phenomenon (or the 'theme' of Reverse Mathe in many branches of ordinary mathematics: When the theorem is proved from the right the axioms can be proved from the theorem. In this paper, we give an instance that the of Reverse Mathematics does not apply to the lightface statements, by demonstrating statement that all Σ11 partitions are Ramsey is deducible over the system ATR0 from the of Σ11 monotone inductive definition, but the reversal is not deducible over ATR0.
UR - http://www.scopus.com/inward/record.url?scp=45149147060&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=45149147060&partnerID=8YFLogxK
U2 - 10.1016/0168-0072(89)90066-3
DO - 10.1016/0168-0072(89)90066-3
M3 - Article
AN - SCOPUS:45149147060
VL - 42
SP - 81
EP - 104
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
SN - 0168-0072
IS - 1
ER -