Geodesic
A~normal form theorem for second-order classical logic with an axiom of choice
Izvestiya. Mathematics , Tome 32 (1989) no. 3, pp. 587-605

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A cut-elimination theorem for the second-order logic with an axiom of choice of type $0,1$ or $1,1$ is proved. In the first case the Päppinghaus scheme is applied; in the second the calculus with an epsilon-symbol for predicates is used. Bibliography: 5 titles. 
@article{IM2_1989_32_3_a6,
     author = {G. E. Mints},
     title = {A~normal form theorem for second-order classical logic with an axiom of choice},
     journal = {Izvestiya. Mathematics },
     pages = {587--605},
     publisher = {mathdoc},
     volume = {32},
     number = {3},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1989_32_3_a6/}
}
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G. E. Mints. A~normal form theorem for second-order classical logic with an axiom of choice. Izvestiya. Mathematics , Tome 32 (1989) no. 3, pp. 587-605. http://geodesic.mathdoc.fr/item/IM2_1989_32_3_a6/