کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5778102 | 1633424 | 2008 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Determinacy in third order arithmetic
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
منطق ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We investigate the strength of open and clopen determinacy of perfect information games with real number moves in the context of third order arithmetic. This work is conducted in a framework developed in 2015 by Schweber [12], who showed that in this setting, open determinacy (Σ1R-DET) is not implied by clopen determinacy (Î1R-DET). We give a new forcing-free proof of this result by isolating a level of L witnessing this separation. We give a notion of β-absoluteness in the context of third-order arithmetic, and show that this level of L is a β-model; combining this with our previous results on the strength of Borel determinacy, we show that Σ40-DET, determinacy for games on Ï with Σ40 payoff, is sandwiched between Σ1R-DET and Î1R-DET in terms of β-consistency strength.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 168, Issue 11, November 2017, Pages 2008-2021
Journal: Annals of Pure and Applied Logic - Volume 168, Issue 11, November 2017, Pages 2008-2021
نویسندگان
Sherwood Hachtman,