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• CommentRowNumber1.
• CommentAuthorEric
• CommentTimeOct 25th 2009

I weakened the definition of covering relation for directed graphs so that $(x,y)$ satisfy the covering relation if their is an edge $x\to y$ and no other path from $x$ to $y$. The condition that there is no $z$ with edges $x\to z$ and $z\to y$ is too strong.

• CommentRowNumber2.
• CommentAuthorTobyBartels
• CommentTimeOct 25th 2009

You mean too weak? Yes, that sounds quite reasonable, even before considering whether it gives us the right definition of Hasse diagram.