# Download PDF by Herbert B. Enderton: A Mathematical Introduction to Logic (2nd Edition)

By Herbert B. Enderton

ISBN-10: 0122384520

ISBN-13: 9780122384523

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**Extra info for A Mathematical Introduction to Logic (2nd Edition)**

**Sample text**

Then S is inductive, and so equals C. I x. Now for the details. 1. As above, let S = {XE C I for at most one z, (x, z) E h] = {x E C I all acceptable functions defined at x agree there] Toward showing that S is inductive, first consider some x in B. Suppose that vl and v2 are acceptable functions defined at x; we seek to show that vl(x) = v2(x). But condition (it) tells us that both vl (x) and v2 (x) must equal h(x), so indeed vl (x) = v2 (x). This shows that x E S ; since x was an arbitrary member of B we have B 5 S .

We claim that this extension has gained us nothing, in the following precise sense: For any wff in the extended language, there is a tautologically equivalent wff in the original language. ) We will prove this (in a more general situation) below; here we just note that it relies on the fact that (#My) is tautologically equivalent to (We note parenthetically that our insistence that iJ((#olBy)) be calculable from @(a), iJ(B), iJ( y )) plays a definite role here. ) In generalizing the foregoing example, the formal language will be more of a hindrance than a help.

Jkall less than i. Give the correct definition of C* and show that C* = C,. 5 Sentential Connectives We have thus far employed five sentential connective symbols. Even in the absence of a general definition of "connective," it is clear that the five familiar ones are not the only ones possible. Would we gain anything by adding more connectives to the language? Would we lose anything by omitting some we already have? In this section we make these questions precise and give some answers. First consider an informal example.

### A Mathematical Introduction to Logic (2nd Edition) by Herbert B. Enderton

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