Weak determinacy and iterations of inductive definitions. (English) Zbl 1157.03035

Ould MedSalem, MedYahya; Tanaka, Kazuyuki

Chong, Chitat (ed.) et al., Computational prospects of infinity. Part II: Presented talks. Selected papers of the workshop, June 20–August 15, 2005. Hackensack, NJ: World Scientific (ISBN 978-981-279-654-7/hbk). Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore 15, 333-353 (2008).

Working in ACA\(_0 + \Pi^1_3\)-TI, the authors show that the determinacy principle \(\Delta^0_3\)-Det is equivalent to \([\Sigma^1_1]^{\text{TR}}\)-ID, an axiom which asserts the existence of prewellorderings constructed by iterative applications of transfinite sequences of \(\Sigma^1_1\) operators.
This extends their earlier work on determinacy in [“\(\Delta^0_3\)-determinacy, comprehension and induction”, J. Symb. Log. 72, No. 2, 452–462 (2007; Zbl 1118.03056)].
For the entire collection see [Zbl 1142.03003].

Reviewer: Jeffry L. Hirst (Boone)

MSC:

03F35	Second- and higher-order arithmetic and fragments
03E60	Determinacy principles

Keywords:

determinacy; reverse mathematics; inductive definition

Citations:

Zbl 1118.03056