1969•Journal of Symbolic LogicRequires access

Definability in the monadic second-order theory of successor

J. Richard Buchi, Lawrence H. Landweber

Abstract

Let be a relational system whereby D is a nonempty set and P1 is an m1-ary relation on D. With we associate the (weak) monadic second-order theory consisting of the first-order predicate calculus with individual variables ranging over D; monadic predicate variables ranging over (finite) subsets of D; monadic predicate quantifiers; and constants corresponding to P1, P2, …. We will often use ambiguously to mean also the set of true sentences of .

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Key concepts: Monadic predicate calculus, Predicate (mathematical logic), Successor cardinal, Mathematics, First-order logic, Second-order logic, Predicate variable, Discrete mathematics