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Algebra Logika, 2007, Volume 46, Number 1, Pages 83–102 (Mi al11)  

Distributive lattices of numberings

Z. G. Khisamiev


Abstract: We study into a semilattice of numberings generated by a given fixed numbering via operations of completion and taking least upper bounds. It is proved that, except for the trivial cases, this semilattice is an infinite distributive lattice every principal ideal in which is finite. The least upper and the greatest lower bounds in the semilattice are invariant under extensions in the semilattice of all numberings. Isomorphism types for the semilattices in question are in one-to-one correspondence with pairs of cardinals the first component of which is equal to the cardinality of a set of non-special elements, and the second – to the cardinality of a set of special elements, of the initial numbering.

Keywords: numbering, complete numbering, completion, special element, upper semilattice of numberings.

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English version:
Algebra and Logic, 2007, 46:1, 50–61

Bibliographic databases:

UDC: 510.5
Received: 18.11.2004
Revised: 19.06.2006

Citation: Z. G. Khisamiev, “Distributive lattices of numberings”, Algebra Logika, 46:1 (2007), 83–102; Algebra and Logic, 46:1 (2007), 50–61

Citation in format AMSBIB
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\paper Distributive lattices of numberings
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\pages 83--102
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\pages 50--61
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