Theory of relations
The first part of this book concerns the present state of the theory of chains (= total or linear orderings), in connection with some refinements of Ramsey's theorem, due to Galvin and Nash-Williams. This leads to the fundamental Laver's embeddability theorem for scattered chains, using Na...
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| Format: | eBook |
| Language: | English |
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Amsterdam
North-Holland
1986, 1986
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| Series: | Studies in logic and the foundations of mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Elsevier eBook collection Mathematics - Collection details see MPG.ReNa |
| Summary: | The first part of this book concerns the present state of the theory of chains (= total or linear orderings), in connection with some refinements of Ramsey's theorem, due to Galvin and Nash-Williams. This leads to the fundamental Laver's embeddability theorem for scattered chains, using Nash-Williams' better quasi-orderings, barriers and forerunning. The second part (chapters 9 to 12) extends to general relations the main notions and results from order-type theory. An important connection appears with permutation theory (Cameron, Pouzet, Livingstone and Wagner) and with logics (existence criterion of Pouzet-Vaught for saturated relations). The notion of bound of a relation (due to the author) leads to important calculus of thresholds by Frasnay, Hodges, Lachlan and Shelah. The redaction systematically goes back to set-theoretic axioms and precise definitions (such as Tarski's definition for finite sets), so that for each statement it is mentioned either that ZF axioms suffice, or what other axioms are needed (choice, continuum, dependent choice, ultrafilter axiom, etc.) |
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| Item Description: | Translation of: Théorie des relations. - Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002 |
| Physical Description: | xii, 397 pages |
| ISBN: | 9780444878656 0444878653 9780080960418 |