A.Heyting, Die formalen Regeln der intuitionistische Logik und Mathematik, Preuss. Akad. der Wiss., 1930  Home/Search   Document Not in Database   Summary   Related Articles   Check

....A formula is valid, or a tautology, if it gets value True under any valuation. 2 3 Hilbert type axiomatic systems, Gentzen s sequent calculus and Gentzen s natural deduction Axiomatic deduction systems are called formalizations of Hilbert (also Frege, Russell, or Heyting) type. See [4] i [3]. Their common characteristic feature is the concept of proof as a finite sequence of formulae each of which is either an axiom or follows from the earlier ones by one of the accepted rules of deduction. In the case of classical propositional calculus it is enough to accept just one rule modus ....

A.Heyting, Die formalen Regeln der intuitionistische Logik und Mathematik, Preuss. Akad. der Wiss., 1930

....the usual definition of Tarski s satisfaction relation between structures, formulae and valuations of free variables. See, e.g. Shoenfield [13] 3 Hilbert type axiomatic systems Axiomatic deduction systems are called formalizations of Hilbert (also Frege, Russell, or Heyting) type. See [7] i [6]. Their common characteristic feature is the concept of proof as a finite sequence of formulae each of which is either an axiom or follows from the earlier ones by one of the accepted rules of deduction. In the case of classical propositional calculus it is enough to accept just one rule modus ....

A.Heyting, Die formalen Regeln der intuitionistische Logik und Mathematik, Preuss. Akad. der Wiss., 1930

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