Abstract
The theory of infinite games with slightly imperfect information has been developed for games with finitely and countably many moves. In this paper, we shift the discussion to games with uncountably many possible moves, introducing the axiom of real Blackwell determinacy \({\mathsf{Bl-AD}_\mathbb{R}}\) (as an analogue of the axiom of real determinacy \({\mathsf{AD}_\mathbb{R}}\)). We prove that the consistency strength of \({\mathsf{Bl-AD}_\mathbb{R}}\) is strictly greater than that of AD.
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Acknowledgments
The research of the first author was supported by a GLoRiClass fellowship funded by the European Commission (Early Stage Research Training Mono-Host Fellowship MEST-CT-2005-020841) and a grant by the Japan Society for the Promotion of Science; the work of the second author was done while he was at the Vrije Universiteit Amsterdam; the work of the third author was partially supported by the DFG-NWO Bilateral Grant KO 1353-5/1/DN 62-630. The authors should like to thank Vincent Kieftenbeld (Edwardsville IL) for discussions in the early phase of this project. They are grateful to an anonymous referee for suggesting a simpler proof of Lemma 11.
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Ikegami, D., de Kloet, D. & Löwe, B. The axiom of real Blackwell determinacy. Arch. Math. Logic 51, 671–685 (2012). https://doi.org/10.1007/s00153-012-0291-x
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DOI: https://doi.org/10.1007/s00153-012-0291-x