اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBounded variation and the strength of Hellys selection theorem
166
0
0.0
(
0
)
نشر من قبل
Alexander P. Kreuzer
تاريخ النشر
2013
مجال البحث
الهندسة المعلوماتية
والبحث باللغة
English
تأليف
Alexander P. Kreuzer
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We analyze the strength of Hellys selection theorem HST, which is the most important compactness theorem on the space of functions of bounded variation. For this we utilize a new representation of this space intermediate between $L_1$ and the Sobolev space W1,1, compatible with the, so called, weak* topology. We obtain that HST is instance-wise equivalent to the Bolzano-Weierstrass principle over RCA0. With this HST is equivalent to ACA0 over RCA0. A similar classification is obtained in the Weihrauch lattice.
قيم البحث
اقرأ أيضاً
We undertake the study of size-change analysis in the context of Reverse Mathematics. In particular, we prove that the SCT criterion is equivalent to $Sigma^0_2$-induction over RCA$_0$.
The Gratzer-Schmidt theorem of lattice theory states that each algebraic lattice is isomorphic to the congruence lattice of an algebra. We study the reverse mathematics of this theorem. We also show that the set of indices of computable lattices th
at are complete is $Pi^1_1$-complete; the set of indices of computable lattices that are algebraic is $Pi^1_1$-complete; the set of compact elements of a computable lattice is $Pi^{1}_{1}$ and can be $Pi^1_1$-complete; and the set of compact elements of a distributive computable lattice is $Pi^{0}_{3}$, and there is an algebraic distributive computable lattice such that the set of its compact elements is $Pi^0_3$-complete.
In this paper, we show that $mathrm{RT}^{2}+mathsf{WKL}_0$ is a $Pi^{1}_{1}$-conservative extension of $mathrm{B}Sigma^0_3$.
We study the reverse mathematics and computability-the-o-re-tic strength of (stable) Ramseys Theorem for pairs and the related principles COH and DNR. We show that SRT$^2_2$ implies DNR over RCA$_0$ but COH does not, and answer a question of Mileti b
y showing that every computable stable $2$-coloring of pairs has an incomplete $Delta^0_2$ infinite homogeneous set. We also give some extensions of the latter result, and relate it to potential approaches to showing that SRT$^2_2$ does not imply RT$^2_2$.
In this paper we continue the study, from Frittaion, Steila and Yokoyama (2017), on size-change termination in the context of Reverse Mathematics. We analyze the soundness of the SCT method. In particular, we prove that the statement any program whic
h satisfies the combinatorial condition provided by the SCT criterion is terminating is equivalent to $mathrm{WO}(omega_3)$ over $mathsf{RCA_0}$
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
