TY - JOUR
T1 - Weak axioms of determinacy and subsystems of analysis II (∑02 games)
AU - Tanaka, Kazuyuki
PY - 1991/4/15
Y1 - 1991/4/15
N2 - In [10], we have shown that the statement that all ∑11 partitions are Ramsey is deducible over ATR0 from the axiom of ∑11 monotone inductive definition,but the reversal needs P{cyrillic}11-CA0 rather than ATR0. By contrast, we show in this paper that the statement that all ∑02 games are determinate is also deducible over ATR0 from the axiom of ∑11 monotone inductive definition, but the reversal is provable even in ACA0. These results illuminate the substantial differences among lightface theorems which can not be observed in boldface.
AB - In [10], we have shown that the statement that all ∑11 partitions are Ramsey is deducible over ATR0 from the axiom of ∑11 monotone inductive definition,but the reversal needs P{cyrillic}11-CA0 rather than ATR0. By contrast, we show in this paper that the statement that all ∑02 games are determinate is also deducible over ATR0 from the axiom of ∑11 monotone inductive definition, but the reversal is provable even in ACA0. These results illuminate the substantial differences among lightface theorems which can not be observed in boldface.
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U2 - 10.1016/0168-0072(91)90045-N
DO - 10.1016/0168-0072(91)90045-N
M3 - Article
AN - SCOPUS:27544438867
VL - 52
SP - 181
EP - 193
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
SN - 0168-0072
IS - 1-2
ER -