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Full Idea
'Theorem': given a derivation of the sentence φ from the axioms of the theory T using the background logical proof system, we will say that φ is a 'theorem' of the theory. Standard abbreviation is T |- φ.
Gist of Idea
A 'theorem' of a theory is a sentence derived from the axioms using the proof system
Source
Peter Smith (Intro to Gödel's Theorems [2007], 03.4)
Book Ref
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.23
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| 16906 | The primitive simples of arithmetic are the essence, determining the subject, and its boundaries [Frege, by Jeshion] |
| 16865 | 'Theorems' are both proved, and used in proofs [Frege] |
| 17807 | To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry] |
| 10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
| 14620 | Theories in logic are sentences closed under consequence, but in truth discussions theories have axioms [Fine,K] |
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| 16310 | A theory is some formulae and all of their consequences [Halbach] |