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5. Theory of Logic / K. Features of Logics / 7. Decidability

[are positive or negative answers always possible?]

7 ideas
Validity is provable, but invalidity isn't, because the model is infinite [Church, by McGee]
Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton]
'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P]
A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P]
Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P]
'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]
Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]