Mathematical Logic Quarterly 48 (4):525-532 (2002)
| Abstract |
A partially ordered set is called k-homogeneous if any isomorphism between k-element subsets extends to an automorphism of . Assuming the set-theoretic assumption ⋄, it is shown that for each k, there exist partially ordered sets of size ϰ1 which embed each countable partial order and are k-homogeneous, but not -homogeneous. This is impossible in the countable case for k ≥ 4
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| Keywords | homogeneous partial order diamond |
| Categories | (categorize this paper) |
| DOI | 10.1002/1521-3870(200211)48:4 |
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