Decidability and $\aleph_0$-Categoricity of Theories of Partially Ordered Sets
Schmerl, James H.
J. Symbolic Logic, Tome 45 (1980) no. 1, p. 585-611 / Harvested from Project Euclid
This paper is primarily concerned with $\aleph_0$-categoricity of theories of partially ordered sets. It contains some general conjectures, a collection of known results and some new theorems on $\aleph_0$-categoricity. Among the latter are the following. Corollary 3.3. For every countable $\aleph_0$-categorical $\mathfrak{U}$ there is a linear order of $A$ such that $(\mathfrak{U}, <)$ is $\aleph_0$-categorical. Corollary 6.7. Every $\aleph_0$-categorical theory of a partially ordered set of finite width has a decidable theory. Theorem 7.7. Every $\aleph_0$-categorical theory of reticles has a decidable theory. There is a section dealing just with decidability of partially ordered sets, the main result of this section being. Theorem 8.2. If $(P, <)$ is a finite partially ordered set and $K_P$ is the class of partially ordered sets which do not embed $(P, <)$, then $\mathrm{Th}(K_P)$ is decidable iff $K_P$ contains only reticles.
Publié le : 1980-09-14
Classification: 
@article{1183740623,
     author = {Schmerl, James H.},
     title = {Decidability and $\aleph\_0$-Categoricity of Theories of Partially Ordered Sets},
     journal = {J. Symbolic Logic},
     volume = {45},
     number = {1},
     year = {1980},
     pages = { 585-611},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183740623}
}
Schmerl, James H. Decidability and $\aleph_0$-Categoricity of Theories of Partially Ordered Sets. J. Symbolic Logic, Tome 45 (1980) no. 1, pp.  585-611. http://gdmltest.u-ga.fr/item/1183740623/