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One conservative extension of formal mathematic analysis with a scheme of dependent choice
Matematičeskie zametki, Tome 22 (1977) no. 1, pp. 61-68 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper studies an extension of classical analysis, the language of which is obtained by adding to the language of analysis a two-place predicate symbol $\rho$. To the axioms of this extension, in addition to all the axioms of analysis (a convolution scheme is selected for all the formulas of the new language), there also belong a series of axioms asserting that relationship $\rho$ completely orders the class of all sets of natural numbers. It is proven that the theory described herein is a conservative extension of analysis with a scheme of dependent choice. 
@article{MZM_1977_22_1_a6,
     author = {A. M. Levin},
     title = {One conservative extension of formal mathematic analysis with a~scheme of dependent choice},
     journal = {Matemati\v{c}eskie zametki},
     pages = {61--68},
     year = {1977},
     volume = {22},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_1_a6/}
}
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A. M. Levin. One conservative extension of formal mathematic analysis with a scheme of dependent choice. Matematičeskie zametki, Tome 22 (1977) no. 1, pp. 61-68. http://geodesic.mathdoc.fr/item/MZM_1977_22_1_a6/