On formulas of one variable in intuitionistic propositional calculus
Copyright policy )On formulas of one variable in intuitionistic propositional calculus
McKinsey and Tarski [3] described Gödel's proof that the number of Brouwerian-algebraic functions is infinite. They gave an example of a sequence of infinitely many distinct Brouwerian-algebraic functions of one argument, which means that there are infinitely many non-equivalent formulas of one variable in the intuitionistic propositional calculus LJ of Gentzen [1]. However they did not completely characterize such formulas. In § 1 of this note, we define a sequence of basic formulas P∞(X), P0(X), P1(X), … and prove the following theorems.
lattice of equivalence classes, formulae of intuitionistic propositional logic (IPC) in one variable, Mathematical logic and foundations
lattice of equivalence classes, formulae of intuitionistic propositional logic (IPC) in one variable, Mathematical logic and foundations
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