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Delbrin Ahmed (SZTE): Conditions satisfied by clone lattices

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Wednesday, 20. March 2019, 10:00 - 12:00
Abstract. The set of all clones on a given set forms a lattice, which is completely described only when the underlying set has just two elements. On sets with at least three elements the clone lattice is uncountable and its structure seems very complicated; in particular, every finite lattice embeds into the clone lattice (if the underlying set has at least 4 elements), hence the clone lattices do not satisfy any nontrivial identity or quasi-identity. In view of this fact, it might be somewhat surprising that the lattice of clones on a finite set satisfies some nontrivial "infinitary quasi-identities". This was proved by Andrei Bulatov [1], and the speaker will present the proof as part of the clone theory PhD course (MDPT3105). The talk will include the necessary background on clones, including the proof of the uncountability of the clone lattice.

[1] Andrei A. Bulatov, Conditions satisfied by clone lattices, Algebra Universalis 46 (2001), 237--241.
Location : Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged


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