ℵ₀-categoricity of partially ordered sets of width 2.

Schmerl, J. H.

doi:10.1090/S0002-9939-1977-0439615-0

$\aleph _{0}$-categoricity of partially ordered sets of width $2.$
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Proc. Amer. Math. Soc. 63 (1977), 299-305 Request permission

Abstract:

A result of J. Rosenstein is that every ${\aleph _0}$-categorical theory of linear order is finitely axiomatizable. We extend this to the case of partially ordered sets of width 2.

References

R. Amit and S. Shelah, The complete finitely axiomatized theories of order are dense, Israel J. Math. 23 (1976), no. 3-4, 200–208. MR 485315, DOI 10.1007/BF02761800
R. P. Dilworth, A decomposition theorem for partially ordered sets, Ann. of Math. (2) 51 (1950), 161–166. MR 32578, DOI 10.2307/1969503
S. Feferman and R. L. Vaught, The first order properties of products of algebraic systems, Fund. Math. 47 (1959), 57–103. MR 108455, DOI 10.4064/fm-47-1-57-103
Joseph G. Rosenstein, $\aleph _{0}$-categoricity of linear orderings, Fund. Math. 64 (1969), 1–5. MR 242652, DOI 10.4064/fm-64-1-1-5
C. Ryll-Nardzewski, On the categoricity in power $\leq \aleph _{0}$, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 7 (1959), 545–548. (unbound insert) (English, with Russian summary). MR 0111681
James H. Schmerl, On $\aleph _{0}$-categoricity and the theory of trees, Fund. Math. 94 (1977), no. 2, 121–128. MR 437337, DOI 10.4064/fm-94-2-121-128

categoricity of partially ordered sets of width

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