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Record Nr. |
UNINA9910827858103321 |
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Autore |
Warren Richard <1967-> |
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Titolo |
The structure of k-CS-transitive cycle-free partial orders / / Richard Warren |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 1997 |
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ISBN |
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Descrizione fisica |
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1 online resource (183 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 614 |
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Disciplina |
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Soggetti |
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Partially ordered sets |
Combinatorial set theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"September 1997, volume 129, number 614 (second of 4 numbers)." |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""Contents""; ""1 Extended Introduction""; ""1.1 Introduction""; ""1.2 Cycle-free partial orders""; ""1.3 Homogeneous structures""; ""1.4 k-connected set transitivity""; ""1.5 Finite and infinite chain CFPO[sub(s)]""; ""1.6 Elements of the classification""; ""1.7 Further work""; ""2 Preliminaries""; ""2.1 Introduction""; ""2.2 Dedekind-complete partial orders""; ""2.3 Cycle-free partial orders""; ""2.4 Concerning paths, and the density lemma""; ""2.5 Substructures, cones, and their extensions""; ""2.6 Convex cycle-free partial orders""; ""3 Properties of k-CS-transitive CFPOs"" |
""3.1 Introduction""""3.2 k-CS-transivity and k-CS-homogeneity""; ""3.3 The infinite chain case""; ""3.4 The finite chain case and the bipartite theorem""; ""3.5 Sporadic and skeletal cycle-free partial orders""; ""4 Constructing CFPOs""; ""4.1 Introduction""; ""4.2 The completion theorem (Part one)""; ""4.3 The completion theorem (Part two)""; ""4.4 Useful results concerning M,M[sup(D)] and M""; ""5 Characterization and Isomorphism Theorems""; ""5.1 Introduction""; ""5.2 Characterizations in the infinite chain case""; ""5.3 The isomorphism theorems and their corollaries"" |
""6 Classification of skeletal CFPOs (Part 1)""""6.1 Introduction""; ""6.2 Case A: â??Ram(M) = â??Ram(M)""; ""6.3 Case B: â??Ram(M)â?©â??Ram(M) = Ï?and Ram(M) is dense""; ""6.4 Covering orders""; ""6.5 Case C: |
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Fully covered cycle-free partial orders""; ""6.6 Case D: Partially covered cycle-free partial orders""; ""6.7 Subcase D1: The cycle-free partial orders D[sup(d,u,u')][sub(Ï?)]""; ""6.8 Subcase D2: The cycle-free partial orders e[sup(d,u,u')][sub(Ï?)]""; ""6.9 Subcase D3: The cycle-free partial orders F[sup(d,u,u')][sub(Ï?,z)]""; ""6.10 Summary "" |
""7 Classification of skeletal CFPOs (Part 2)""""7.1 Introduction""; ""7.2 The cycle-free partial orders g[sup(u,d,u',d')][sub(z)]""; ""7.3 Case 2: The cycle-free partial orders H[sup(u,d,u',d')][sub(z)]""; ""7.4 An empty case""; ""7.5 Case 3: The remaining few""; ""7.6 Conclusions in the skeletal case""; ""Appendix: Sporadic Cycle-free Partial Orders""; ""A.1 Introduction""; ""A.2 The classification""; ""A.3 Conclusions"" |
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