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### Single Idea 10155

#### [catalogued under 5. Theory of Logic / K. Features of Logics / 7. Decidability]

Full Idea

In 1936 Church showed that Principia Mathematica is undecidable if it is ω-consistent, and a year later Rosser showed that Peano Arithmetic is undecidable, and any consistent extension of it.

Gist of Idea

Both Principia Mathematica and Peano Arithmetic are undecidable

Source

Feferman / Feferman (Alfred Tarski: life and logic [2004], Int IV)

Book Reference

Feferman,S/Feferman,A.B.: 'Alfred Tarski: life and logic' [CUP 2008], p.193