Necessary use of \(\Sigma ^1_{1}\) induction in a reversal. (English) Zbl 1218.03005

In an earlier paper [J. Math. Log. 8, No. 1, 93–119 (2008; Zbl 1186.03071)], the author showed that, in \(\text{RCA}_0\)+\(\Sigma^1_1\)-induction, Jullien’s indecomposability theorem implies weak \(\Delta^1_1\)-choice. In the paper under review he provides a model which shows that it is not possible to obtain this result when weakening \(\Sigma^1_1\)-induction to \(\Delta^1_1\)-induction.


03B30 Foundations of classical theories (including reverse mathematics)
03E75 Applications of set theory
03F35 Second- and higher-order arithmetic and fragments


Zbl 1186.03071
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