NDLI: On a semilattice of numberings

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On a semilattice of numberings

Content Provider	Springer Nature Link
Author	Puzarenko, V. G.
Copyright Year	2010
Abstract	We study some properties of a $$ \mathfrak{c} $$ -universal semilattice $$ \mathfrak{A} $$ with the cardinality of the continuum, i.e., of an upper semilattice of m-degrees. In particular, it is shown that the quotient semilattice of such a semilattice modulo any countable ideal will be also $$ \mathfrak{c} $$ -universal. In addition, there exists an isomorphism onto some ideal of the semilattice $$ \mathfrak{A} $$ such that $$ {\mathfrak{A} \mathord{\left/ {\vphantom {\mathfrak{A} {\iota \left( \mathfrak{A} \right)}}} \right. -} {\iota \left( \mathfrak{A} \right)}} $$ will be also $$ \mathfrak{c} $$ -universal. Furthermore, a property of the group of its automorphisms is obtained. To study properties of this semilattice, the technique and methods of admissible sets are used. More exactly, it is shown that the semilattice of mΣ-degrees $$ L_{m\Sigma }^{\mathbb{H}\mathbb{F}\left( S \right)} $$ on the hereditarily finite superstructure $$ \mathbb{H}\mathbb{F} $$ (S) over a countable set S will be a $$ \mathfrak{c} $$ -universal semilattice with the cardinality of the continuum.
Starting Page	128
Ending Page	154
Page Count	27
File Format	PDF
ISSN	10551344
Journal	Siberian Advances in Mathematics
Volume Number	20
Issue Number	2
e-ISSN	19348126
Language	English
Publisher	Allerton Press, Inc.
Publisher Date	2010-05-28
Publisher Place	Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	computably enumerable set admissible set $\mathbb{A}$ -numbering mΣ-reducibility hereditarily finite superstructure natural ordinal upper semilattice a $\mathfrak{c}$ -universal semilattice Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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