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Ideas for 'works', 'Logic in Mathematics' and 'Alfred Tarski: life and logic'

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7 ideas

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation

16866

Tracing inference backwards closes in on a small set of axioms and postulates [Frege]

16868

The essence of mathematics is the kernel of primitive truths on which it rests [Frege]

16871

A truth can be an axiom in one system and not in another [Frege]

16870

Axioms are truths which cannot be doubted, and for which no proof is needed [Frege]

5. Theory of Logic / K. Features of Logics / 4. Completeness

10161

If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman]

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

10156

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

10155

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