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A set is amorphous, if it is not a union of two disjoint infinite subsets. The following variants of the Tychonoff product theorem are investigated in the hierarchy of weak choice principles. TA1: An amorphous power of a compactT
2 space is compact. TA2: An amorphous power of a compactT
The purpose of this article is to establish the relation between the new concepts ofΠ
-Logic, introduced by Girard [G4] and the traditional approach of cut elimination, in particular with respect to the bounds obtained: The bounds for the cut elimination theorem are given explicitly in the...
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