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Full Idea
Instead of demonstrations which are either axioms, or follow from axioms by rules, we can have one ever-growing sequence of formulas of the form 'Axioms |- ______', where the blank is filled by Axioms, then Lemmas, then Theorems, then Corollaries.
Gist of Idea
We can build one expanding sequence, instead of a chain of deductions
Source
John P. Burgess (Philosophical Logic [2009], 5.3)
Book Ref
Burgess,John P.: 'Philosophical Logic' [Princeton 2009], p.105
13759 | Each line of a sequent calculus is a conclusion of previous lines, each one explicitly recorded [Bostock] |
13760 | A sequent calculus is good for comparing proof systems [Bostock] |
15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess] |
15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |