The logic of negationless mathematics
Compositio Mathematica, Tome 11 (1953), pp. 204-270. 
@article{CM_1953__11__204_0,
     author = {Vredenduin, P. G. J.},
     title = {The logic of negationless mathematics},
     journal = {Compositio Mathematica},
     pages = {204--270},
     publisher = {Kraus Reprint},
     volume = {11},
     year = {1953},
     mrnumber = {61566},
     zbl = {0053.20201},
     language = {en},
     url = {http://www.numdam.org/item/CM_1953__11__204_0/}
}
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Vredenduin, P. G. J. The logic of negationless mathematics. Compositio Mathematica, Tome 11 (1953), pp. 204-270. http://www.numdam.org/item/CM_1953__11__204_0/