Finitely Generated Magari Algebras and Arithmetic
Lex Hendriks, Dick de Jongh
Abstract:
Some consequences are studied of Shavrukov's theorem regarding
the Magari algebras (diagonalizable algebras) that are embeddable in
the Magari algebra of formal arithmetical theories. Semantic characĀ
terizations of faithfully interpretable modal propositional theories in a
finite number of propositional letters are given, in particular for finitely
axiomatizable ones. Supported by this theory computer aided calculations
on the theories of lowest complexity in one propositional letter
were executed leading to a complete list of 62 formulas that axiomatize
such theories under which the 8 maximal ones of particular interest.