NDLI: Poset algebras over well quasi-ordered posets

Content Provider	Springer Nature Link
Author	Bonnet, Robert Abraham, Uri Kubiś, Wiesław
Copyright Year	2008
Abstract	A new class of partial order-types, class $${\mathcal{G}}^{+}_{bqo}$$ is defined and investigated here. A poset P is in the class $${\mathcal{G}}^{+}_{bqo}$$ iff the poset algebra F(P) is generated by a better quasi-order G that is included in L(P).The free Boolean algebra F(P) and its free distributive lattice L(P) have been defined in [ABKR]. The free Boolean algebra F(P) contains the partial order P and is generated by it: F(P) has the following universal property. If B is any Boolean algebra and f is any order-preserving map from P into a Boolean algebra B, then f can be extended to a homomorphism $${\hat f}$$ of F(P) into B. We also define L(P) as the sublattice of F(P) generated by P.We prove that if P is any well quasi-ordering, then L(P) is well founded, and is a countable union of well quasi-orderings.We prove that the class $${\mathcal{G}}^{+}_{bqo}$$ is contained in the class of well quasi-ordered sets. We prove that $${\mathcal{G}}^{+}_{bqo}$$ is preserved under homomorphic image, finite products, and lexicographic sum over better quasi-ordered index sets. We prove also that every countable well quasi-ordered set is in $${\mathcal{G}}^{+}_{bqo}$$ . We do not know, however if the class of well quasi-ordered sets is contained in $${\mathcal{G}}^{+}_{bqo}$$ . Additional results concern homomorphic images of posets algebras.
Ending Page	286
Page Count	24
Starting Page	263
File Format	PDF
ISSN	00025240
e-ISSN	14208911
Journal	algebra universalis
Issue Number	3
Volume Number	58
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2008-05-14
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	poset algebras better quasi-orderings (bqo) Partial order, general Algebra well quasi-orderings (wqo) superatomic Boolean algebras Structure theory Scattered spaces Boolean algebras
Content Type	Text
Resource Type	Article
Subject	Logic Algebra and Number Theory

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