9 ideas
11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read] |
18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt] |
13344 | X follows from sentences K iff every model of K also models X [Tarski] |
11065 | The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna] |
11023 | The logical connectives are 'defined' by their introduction rules [Gentzen] |
11213 | Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen] |
13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |