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Theory of relations. Transl. from the French by P. Clote. (English) Zbl 0593.04001

Studies in Logic and the Foundations of Mathematics, Vol. 118. Amsterdam - New York - Oxford: North-Holland. XII, 397 p. $ 55.25; Dfl. 160.00 (1986).
This is an introductory monograph on the theory of relations. After introductory presentation of set theory, the book goes on to discuss Ramsey theorems, trees, embeddability of orderings, chains, barriers, isomorphisms between relations, age, richness, inexhaustibility, relational systems, permutation groups and orbits, the problem of bounds for a relation, and many other related topics. The author omitted planned chapters on reconstruction and the notion of interval. The writing is clear and extremely concise. Unfortunately, the many interrelationships between the theory of relations and other topics are only hinted at. Many exercises are included as is an extensive bibliography.
Reviewer: A.M.Coyne

MSC:

03-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations
03E20 Other classical set theory (including functions, relations, and set algebra)
08A02 Relational systems, laws of composition
05A99 Enumerative combinatorics