Dalik, Josef Characterizations of certain classes of posets having GS-lattices of a relatively small size. (English) Zbl 0495.06001 Czech. Math. J. 31(106), 433-450 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page MSC: 06A06 Partial orders, general 06B23 Complete lattices, completions 03E40 Other aspects of forcing and Boolean-valued models 68Q45 Formal languages and automata Keywords:principal initial segments; gs-lattice; complete lattice of generating systems; complemented lattice; ordinally indecomposable poset; ascending chain condition; sigma-dense completions; completions of posets Citations:Zbl 0072.021; Zbl 0398.68029 PDF BibTeX XML Cite \textit{J. Dalik}, Czech. Math. J. 31(106), 433--450 (1981; Zbl 0495.06001) Full Text: EuDML OpenURL References: [1] P. Crawley, R. P. Dilworth: Algebraic theory of lattices. Prentice-Hall, New Jersey, 1973. · Zbl 0494.06001 [2] N. Funayama: Imbedding partly ordered sets into infinitely distributive complete lattices. Tohoku Math. Journal 8, N1 (1956), 54-62. · Zbl 0072.02102 [3] D. Scott, R. Solovay: Boolean-valued models of set theory. Proc. of Symp. in Pure Math. 13, II, AMS, Providence R.I., 1971. [4] A. Tarski: Ordinal algebras. North-Holland Amsterdam, 1956. · Zbl 0072.00201 [5] J. Dalík: An embedding problem and its application in linguistics. Arch. Math. (Brno) 3, XIV (1978), 123-138. [6] J. Dalík: Lattices of generating systems. Arch. Math. (Brno) 3, XVI (1980), 137-152. [7] J. Schmidt: Kennzeichnung der Dedekind-MacNeilleschen Hülle einer geordneten Menge. Archiv der Math. (Basel), 1960. · Zbl 0073.03801 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.