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Chapter Seven. Indexed Relational Systems

1981; Elsevier BV; Linguagem: Inglês

10.1016/s0049-237x(08)70879-6

2542-6702

Conflict Management and Negotiation

Publisher SummaryThis chapter discusses indexed relational systems. The axiom system is chosen, because it arises naturally out of the elementary formal system approach, but there are other treatments possible. The most elegant axiomatic development is that of Wagner, Strong, and Friedman. If rec(Ԅ) is a theory with equality, and an effective pairing function, then the recursively enumerable (r.e.) relations provide an indexed relational system, taking the basic functions to be the total functions with r.e. graphs (recursive functions). Again, if rec(Ԅ) is a theory with equality and an effective pairing function, and if ҫ is a relation on set Ҝ, then the relations ≤ҫ provide an indexed relational system. Similarly, the relations ≤ҫ in ω-rec(Ԅ) provide an indexed relational system, where one can take the basic functions to be the recursive ones, provided rec(Ԅ) is a theory with equality and an effective pairing function. The chapter presents a lemma of whose immediate consequence is the Second Recursion theorem and states that a functional indexing could be introduced.