A countable poset with no infinite antichain is constructed that has no 'spine', disproving the Aharoni-Korman (fishbone) conjecture of 1992.
K¨ onig’s duality theorem for infinite bipartite graphs.Journal of the London Mathematical Society 2 , 1 (1984), 1–12
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The Aharoni--Korman conjecture is false
A countable poset with no infinite antichain is constructed that has no 'spine', disproving the Aharoni-Korman (fishbone) conjecture of 1992.