FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1567994500> ?p ?o ?g. }

• W1567994500 abstract "We prove that any infinite sequence of countable series-parallel orders contains an increasing (with respect to embedding) infinite subsequence. This result generalizes Laver's and Corominas' theorems concerning betterquasi-order of the classes of countable chains and trees. Let C be a class of structures and < an order on C. This class is well-quasiordered with respect to < if for any infinite sequence C1,, C2... , Ck, ... in C, there exist i < j such that Ci < Cj. An equivalent definition is: any subset of C has finitely many minimal elements with respect to <. We are mainly concerned here with binary relations, the order < being the embedding order. Thus, 1? < R' when the relation R is embedded in the relation R' (in other words, R is an induced relation of R'). One of the very first results concerning well-quasi-order is Higman's theorem ([5]): the class of finite linear orderings (or chains) labeled by a finite set is well-quasi-ordered with respect to embedding. More precisely, the objects of the class are finite chains whose elements are labeled by a finite set, and embedding means order-preserving and label-preserving injection. For example aabcc embeds into abcabcabc but not into cbacbacba. This result was extended by Kruskal to the class of finite trees [8]. Then Nash-Williams introduced two fundamental tools of the theory: the 'minimal bad sequence' which shortened greatly the proofs concerning well-quasi-order (wqo), and the 'better-quasi-order' (bqo), a strengthening of wqo, which provides a tool to deal with countable structures [11]. Indeed, wqo is no longer an appropriate tool in the infinite case, since one can construct, from Rado's counterexample [13], an infinite set of pairwise incomparable countable subsets of a wqo. Laver proved in [9] that the class of countable chains is better-quasi-ordered (and thus well-quasi-ordered) with respect to einbedding. Later, Corominas [1] extended the result of Kruskal to countable trees: the class of countable trees labeled by a better-quasi-order is better-quasi-ordered with respect to embedding. The proof is in two parts, one devoted to the construction of countable trees, the other concerned with the preservation of better-quasi-order under certain operations. This latter aspect can be found in Milner [10] and Pouzet [12]. In this paper, Pouzet poses the problem of another class of orders, the N-free or series-parallel orders. This class contains the class of trees, and Pouzet was able to prove the wqo Received by the editors October 4, 1995 and, in revised form, January 6, 1998. 1991 Mathematics Subject Classification. Primary 05C20; Secondary 05C05,08A65,05C75." @default.
• W1567994500 created "2016-06-24" @default.
• W1567994500 creator A5033238040 @default.
• W1567994500 date "1999-04-07" @default.
• W1567994500 modified "2023-10-18" @default.
• W1567994500 title "On Better-Quasi-Ordering Countable Series-Parallel Orders" @default.
• W1567994500 cites W1530843743 @default.
• W1567994500 cites W1963780543 @default.
• W1567994500 cites W1985409003 @default.
• W1567994500 cites W2000763343 @default.
• W1567994500 cites W2008739843 @default.
• W1567994500 cites W2018765574 @default.
• W1567994500 cites W2076508310 @default.
• W1567994500 cites W2134705851 @default.
• W1567994500 cites W2138899395 @default.
• W1567994500 cites W2316932045 @default.
• W1567994500 cites W2326386010 @default.
• W1567994500 cites W2777998708 @default.
• W1567994500 cites W296433066 @default.
• W1567994500 doi "https://doi.org/10.1090/s0002-9947-99-02400-9" @default.
• W1567994500 hasPublicationYear "1999" @default.
• W1567994500 type Work @default.
• W1567994500 sameAs 1567994500 @default.
• W1567994500 citedByCount "21" @default.
• W1567994500 countsByYear W15679945002013 @default.
• W1567994500 countsByYear W15679945002014 @default.
• W1567994500 countsByYear W15679945002017 @default.
• W1567994500 countsByYear W15679945002018 @default.
• W1567994500 countsByYear W15679945002020 @default.
• W1567994500 crossrefType "journal-article" @default.
• W1567994500 hasAuthorship W1567994500A5033238040 @default.
• W1567994500 hasBestOaLocation W15679945001 @default.
• W1567994500 hasConcept C10138342 @default.
• W1567994500 hasConcept C108710211 @default.
• W1567994500 hasConcept C110729354 @default.
• W1567994500 hasConcept C114614502 @default.
• W1567994500 hasConcept C118615104 @default.
• W1567994500 hasConcept C134306372 @default.
• W1567994500 hasConcept C137877099 @default.
• W1567994500 hasConcept C138890893 @default.
• W1567994500 hasConcept C143724316 @default.
• W1567994500 hasConcept C151730666 @default.
• W1567994500 hasConcept C154945302 @default.
• W1567994500 hasConcept C162324750 @default.
• W1567994500 hasConcept C162392398 @default.
• W1567994500 hasConcept C182306322 @default.
• W1567994500 hasConcept C2524010 @default.
• W1567994500 hasConcept C2777212361 @default.
• W1567994500 hasConcept C2778112365 @default.
• W1567994500 hasConcept C33923547 @default.
• W1567994500 hasConcept C34388435 @default.
• W1567994500 hasConcept C41008148 @default.
• W1567994500 hasConcept C41608201 @default.
• W1567994500 hasConcept C54355233 @default.
• W1567994500 hasConcept C65180967 @default.
• W1567994500 hasConcept C86803240 @default.
• W1567994500 hasConceptScore W1567994500C10138342 @default.
• W1567994500 hasConceptScore W1567994500C108710211 @default.
• W1567994500 hasConceptScore W1567994500C110729354 @default.
• W1567994500 hasConceptScore W1567994500C114614502 @default.
• W1567994500 hasConceptScore W1567994500C118615104 @default.
• W1567994500 hasConceptScore W1567994500C134306372 @default.
• W1567994500 hasConceptScore W1567994500C137877099 @default.
• W1567994500 hasConceptScore W1567994500C138890893 @default.
• W1567994500 hasConceptScore W1567994500C143724316 @default.
• W1567994500 hasConceptScore W1567994500C151730666 @default.
• W1567994500 hasConceptScore W1567994500C154945302 @default.
• W1567994500 hasConceptScore W1567994500C162324750 @default.
• W1567994500 hasConceptScore W1567994500C162392398 @default.
• W1567994500 hasConceptScore W1567994500C182306322 @default.
• W1567994500 hasConceptScore W1567994500C2524010 @default.
• W1567994500 hasConceptScore W1567994500C2777212361 @default.
• W1567994500 hasConceptScore W1567994500C2778112365 @default.
• W1567994500 hasConceptScore W1567994500C33923547 @default.
• W1567994500 hasConceptScore W1567994500C34388435 @default.
• W1567994500 hasConceptScore W1567994500C41008148 @default.
• W1567994500 hasConceptScore W1567994500C41608201 @default.
• W1567994500 hasConceptScore W1567994500C54355233 @default.
• W1567994500 hasConceptScore W1567994500C65180967 @default.
• W1567994500 hasConceptScore W1567994500C86803240 @default.
• W1567994500 hasLocation W15679945001 @default.
• W1567994500 hasOpenAccess W1567994500 @default.
• W1567994500 hasPrimaryLocation W15679945001 @default.
• W1567994500 hasRelatedWork W114357954 @default.
• W1567994500 hasRelatedWork W1531467827 @default.
• W1567994500 hasRelatedWork W1981356557 @default.
• W1567994500 hasRelatedWork W2018765574 @default.
• W1567994500 hasRelatedWork W2074100739 @default.
• W1567994500 hasRelatedWork W2076508310 @default.
• W1567994500 hasRelatedWork W2110917011 @default.
• W1567994500 hasRelatedWork W2130170273 @default.
• W1567994500 hasRelatedWork W2264894310 @default.
• W1567994500 hasRelatedWork W2283852323 @default.
• W1567994500 hasRelatedWork W2556826017 @default.
• W1567994500 hasRelatedWork W2582512780 @default.
• W1567994500 hasRelatedWork W2923149102 @default.
• W1567994500 hasRelatedWork W2949693431 @default.
• W1567994500 hasRelatedWork W2950577346 @default.
• W1567994500 hasRelatedWork W2951912741 @default.
• W1567994500 hasRelatedWork W2952354628 @default.

• next