Decidability and Undecidability of Extensions of Second (First) Order Theory of (Generalized) Successor
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We study certain first and second order theories which are semantically defined as the sets of all sentences true in certain given structures. Let be a structure where A is a non-empty set, λ is an ordinal, and P α is an n ( α )-ary relation or function 4 on A . With we associate a language L appropriate for which may be a first or higher order calculus. L has an n ( α )-place predicate or function constant P for each α A ; (3) restricted (weak) second-order calculi which contain monadic predicate variables ranging over finite subsets of A .
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