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partially ordered set; interval; selfduality; connectedness

References:

[1] L. Fuchs: **Partially Ordered Algebraic Systems**. Pergamon Press, Oxford, 1963. MR 0171864 | Zbl 0137.02001

[2] V. I. Igoshin: **Lattices of intervals and lattices of convex sublattices of lattices**. Ordered sets and lattices 6 (1980), 69-76. (In Russian.) MR 0945975

[3] V. I. Igoshin: **Identities in interval lattices of lattices**. Contributions to Lattice Theory, Coll. Math. Soc. J. Bolyai 33 (1983), 491-501. MR 0724279 | Zbl 0522.06005

[4] V. I. Igoshin: **On lattices with restrictions on their interval lattices**. Lectures in Universal Algebra, Coll. Math. Soc. J. Bolyai 43 (1986), 209-210. MR 0860266 | Zbl 0598.06003

[5] V. I. Igoshin: **Algebraic characterization of interval lattices**. Uspechi matem. nauk 40 (1985), 205-206. (In Russian.) MR 0795195 | Zbl 0592.06002

[6] V. I. Igoshin: **Interval properties of quasivarieties of lattices**. XVII. Vsesoyuz. alg. konf., Kishinev, 1985, Summaries of lectures, p. 212. (In Russian.)

[7] V. I. Igoshin: **Semimodularity in interval lattices**. Math. Slovaca 38 (1988), 305-308. MR 0978760 | Zbl 0664.06007

[8] V. I. Igoshin: **Selfduality of lattices of intervals of finite lattices**. International conference on algebra dedicated to the memory of A. I. Maltsev, Summaries of lectures on model theory and algebraic systems. Novosibirsk. 1989, p. 48. (In Russian.)

[9] J. Jakubík: **Selfduality of the system of intervals of a partially ordered set**. Czechoslovak Math. J. 41 (1991), 135-140. MR 1087633

[10] J. Jakubík J. Lihová: **Systems of intervals of partially ordered sets**. Math. Slovaca 46 (1996), 355-361. MR 1472629

[11] M. Kolibiar: **Intervals, convex sublattices and subdirect representations of lattices**. Universal Algebra and Applications, Banach Center Publ. Vol. 9. Warsaw, 1982, pp. 335-339. MR 0738826 | Zbl 0506.06003

[12] J. Lihová: **Posets having a selfdual interval poset**. Czechoslovak Math. J. 44 (1994), 523-533. MR 1288170

[13] V. Slavík: **On lattices with isomorphic interval lattices**. Czechoslovak Math. J. 35 (1985), 550-554. MR 0809041