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TZID:Europe/Budapest
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UID:7gd5vk1pl3lhd68fv5nn4bg3rk@google.com
CATEGORIES:{lang hu}Algebra szeminárium{/lang}{lang en}Algebra seminar{/lang}
SUMMARY:Delbrin Ahmed (SZTE): Conditions satisfied by clone lattices
LOCATION:Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:Abstract. The set of all clones on a given set forms a lattice, which is co
mpletely described only when the underlying set has just two elements. On s
ets with at least three elements the clone lattice is uncountable and its s
tructure seems very complicated; in particular, every finite lattice embeds
into the clone lattice (if the underlying set has at least 4 elements), he
nce the clone lattices do not satisfy any nontrivial identity or quasi-iden
tity. In view of this fact, it might be somewhat surprising that the lattic
e of clones on a finite set satisfies some nontrivial "infinitary quasi-ide
ntities". This was proved by Andrei Bulatov [1], and the speaker will prese
nt the proof as part of the clone theory PhD course (MDPT3105). The talk wi
ll include the necessary background on clones, including the proof of the u
ncountability of the clone lattice.

[1] Andrei A. Bulatov, Conditi
ons satisfied by clone lattices, Algebra Universalis 46 (2001), 237--241.
DTSTAMP:20220521T045726Z
DTSTART;TZID=Europe/Budapest:20190320T100000
DTEND;TZID=Europe/Budapest:20190320T120000
SEQUENCE:0
TRANSP:OPAQUE
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