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Single Idea 10088

[filed under theme 5. Theory of Logic / K. Features of Logics / 7. Decidability ]

Full Idea

Any consistent, axiomatized, negation-complete formal theory is decidable.

Gist of Idea

Any consistent, axiomatized, negation-complete formal theory is decidable

Source

Peter Smith (Intro to Gödel's Theorems [2007], 03.6)

Book Ref

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.26

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The 7 ideas with the same theme [are positive or negative answers always possible?]:

18758

Validity is provable, but invalidity isn't, because the model is infinite [Church, by McGee]

9996	Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton]

10080

'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P]

10087

A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P]

10088

Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P]

10156

'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]

10155

Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]