TY - JOUR
T1 - Large intervals in the clone lattice
AU - Goldstern, Martin
AU - Shelah, Saharon
PY - 2009/9
Y1 - 2009/9
N2 - We give three examples of cofinal intervals in the lattice of (local) clones on an infinite set X, whose structure is on the one hand non-trivial but on the other hand reasonably well understood. Specifically, we will exhibit clones l1, l2, l3 such that (1) the interval [l1,]in the lattice of local clones is (as a lattice) isomorphic to {0, 1, 2, ...} under the divisibility relation,(2)the interval in the lattice of local clones is isomorphic to the congruence lattice of an arbitrary semilattice, (3) in the lattice of all clones is isomorphic to the lattice of all filters on X.
AB - We give three examples of cofinal intervals in the lattice of (local) clones on an infinite set X, whose structure is on the one hand non-trivial but on the other hand reasonably well understood. Specifically, we will exhibit clones l1, l2, l3 such that (1) the interval [l1,]in the lattice of local clones is (as a lattice) isomorphic to {0, 1, 2, ...} under the divisibility relation,(2)the interval in the lattice of local clones is isomorphic to the congruence lattice of an arbitrary semilattice, (3) in the lattice of all clones is isomorphic to the lattice of all filters on X.
KW - Dually atomic
KW - Internal isomorphisms
KW - Local clones
KW - Precomplete clones
KW - Ternary discriminator
KW - Ultrafilters
UR - http://www.scopus.com/inward/record.url?scp=77954659726&partnerID=8YFLogxK
U2 - 10.1007/s00012-010-0047-6
DO - 10.1007/s00012-010-0047-6
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AN - SCOPUS:77954659726
SN - 0002-5240
VL - 62
SP - 367
EP - 374
JO - Algebra Universalis
JF - Algebra Universalis
IS - 4
ER -