论文信息 - A note on Dilworth's theorem in the infinite case

A note on Dilworth's theorem in the infinite case

If ℘ is a poset and every antichain is finite, and if the length of the well-founded poset of antichains is less than ω21, then ℘ is the union of countably many chains. We also compute the length of the poset of antichains in the product of two ordinals, αxβ.

Uri Abraham | U. Abraham

[1] R. P. Dilworth,et al. A DECOMPOSITION THEOREM FOR PARTIALLY ORDERED SETS , 1950 .

[2] Philip W. Carruth,et al. Arithmetic of ordinals with applications to the theory of ordered Abelian groups , 1942 .

[3] Micha A. Peles. On dilworth’s theorem in the in finite case , 1963 .

[4] Azriel Levy. Basic set theory , 1979 .

[5] E. C. Milner,et al. The cofinality of a partially ordered set , 1983 .

[6] Micha A. Perles. A proof of dilworth’s decomposition theorem for partially ordered sets , 1963 .

[7] Ben Dushnik,et al. Partially Ordered Sets , 1941 .