ℵ₀-categorical distributive lattices of finite breadth

Schmerl, James H.

doi:10.1090/S0002-9939-1983-0687647-2

$\aleph _{0}$-categorical distributive lattices of finite breadth
HTML articles powered by AMS MathViewer

by James H. Schmerl PDF

Proc. Amer. Math. Soc. 87 (1983), 707-713 Request permission

Abstract:

Every ${\aleph _0}$-categorical distributive lattice of finite breadth has a finitely axiomatizable theory. This result extends the analogous result for partially ordered sets of finite width.

References

Raymond Balbes and Philip Dwinger, Distributive lattices, University of Missouri Press, Columbia, Mo., 1974. MR 0373985
Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
R. P. Dilworth, A decomposition theorem for partially ordered sets, Ann. of Math. (2) 51 (1950), 161–166. MR 32578, DOI 10.2307/1969503
R. P. Dilworth, Some combinatorial problems on partially ordered sets, Proc. Sympos. Appl. Math., Vol. 10, American Mathematical Society, Providence, R.I., 1960, pp. 85–90. MR 0115940
George Grätzer, Lattice theory. First concepts and distributive lattices, W. H. Freeman and Co., San Francisco, Calif., 1971. MR 0321817
Alfred B. Manaster and Joseph G. Rosenstein, Two-dimensional partial orderings: recursive model theory, J. Symbolic Logic 45 (1980), no. 1, 121–132. MR 560230, DOI 10.2307/2273359
Philip Olin, Aleph-zero categorical Stone algebras, J. Austral. Math. Soc. Ser. A 26 (1978), no. 3, 337–347. MR 515751, DOI 10.1017/S1446788700011861
James H. Schmerl, Decidability and $\aleph _{0}$-categoricity of theories of partially ordered sets, J. Symbolic Logic 45 (1980), no. 3, 585–611. MR 583376, DOI 10.2307/2273425
James H. Schmerl, Decidability and finite axiomatizability of theories of $\aleph _{0}$-categorical partially ordered sets, J. Symbolic Logic 46 (1981), no. 1, 101–120. MR 604885, DOI 10.2307/2273263
James H. Schmerl, Arborescent structures. I. Recursive models, Aspects of effective algebra (Clayton, 1979) Upside Down A Book Co., Yarra Glen, Vic., 1981, pp. 226–231. MR 629260