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تسجيل مستخدم جديدEkelands variational principle in weak and strong systems of arithmetic
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We analyze Ekelands variational principle in the context of reverse mathematics. We find that that the full variational principle is equivalent to $Pi^1_1$-${sf CA}_0$, a strong theory of second-order arithmetic, while natural restrictions (e.g.~to compact spaces or continuous functions) yield statements equivalent to weak Konigs lemma (${sf WKL}_0$) and to arithmetical comprehension (${sf ACA}_0$). We also find that the localized version of Ekelands variational principle is equivalent to $Pi^1_1$-${sf CA}_0$ even when restricting to continuous functions. This is a rare example of a statement about continuous functions having great logical strength.
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