## The New Encyclopaedia Britannica, Volume 23 |

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Page 267

Recursive functions and decidability Godefs exact

and

Range. In particular, he discovered that if such a system is a>-consistent ...

Recursive functions and decidability Godefs exact

**theorem**Undecidability of truthand

**theorem**- hood Proof independent of set theory Turing's undecid- ability proofRange. In particular, he discovered that if such a system is a>-consistent ...

Page 269

Godel's original proof of the completeness

second proof above. Consideration may again ... Mm — are not satisfiable; i.e.,

their negations are tautologies (

,j V ..

Godel's original proof of the completeness

**theorem**is closely related to thesecond proof above. Consideration may again ... Mm — are not satisfiable; i.e.,

their negations are tautologies (

**theorems**of the propositional calculus). Thus, ~M,j V ..

Page 559

The part of Godel's

the first step can be carried out fully. Despite the value of the logistic method as a

way of defining exactly the presuppositions of a given portion of mathematics, ...

The part of Godel's

**theorem**that —A, is unprovable but true shows that not eventhe first step can be carried out fully. Despite the value of the logistic method as a

way of defining exactly the presuppositions of a given portion of mathematics, ...

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