Geodesic
The length of joins in Lambek calculus
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2011), pp. 10-14

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In 1992, M. Pentus established a criterion for the existence of a type $C$ such that for given types $A$ and $B$ the sequents $A\to C$ and $B\to C$ are derivable in the Lambek calculus. In this paper we give an algorithm for construction of such a type $C$ (provided it exists) and prove a quadratic upper bound for its length. 
@article{VMUMM_2011_3_a1,
     author = {A. A. Sorokin},
     title = {The length of joins in {Lambek} calculus},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
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     publisher = {mathdoc},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2011_3_a1/}
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A. A. Sorokin. The length of joins in Lambek calculus. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2011), pp. 10-14. http://geodesic.mathdoc.fr/item/VMUMM_2011_3_a1/