Abstract
The principal application of a general theorem proved here shows that for any choice 1≤m≤n≤p of integers there exist metric spacesX andY such that the initialk-segments of their clones of continuous maps coincide exactly whenk≤m, are isomorphic exactly whenk≤n, and are elementarily equivalent exactly whenk≤p.
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Dedicated to Prof. László Fuchs on the occasion of his 70th birthday
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Sichler, J., Trnková, V. On elementary equivalence and isomorphism of clone segments. Period Math Hung 32, 113–128 (1996). https://doi.org/10.1007/BF01879737
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DOI: https://doi.org/10.1007/BF01879737