The decidability of some -categorical theories
The diophantine theory of a ring of analytic functions.
The elementary theory of Abelian groups with m-chains of pure subgroups
The join of equational theories
The -theory of profinite abelian groups
The monadic second-order logic of graphs III : tree-decompositions, minors and complexity issues
The positivity problem for fourth order linear recurrence sequences is decidable
The problem whether each element of a sequence satisfying a fourth order linear recurrence with integer coefficients is nonnegative, referred to as the Positivity Problem for fourth order linear recurrence sequence, is shown to be decidable.
The pseudovariety is hyperdecidable
The recursive sets in certain monadic second order fragments of arithmetic.
The second-order monadic theory of the free inverse monoid is undecidable. (La théorie monadique du second ordre du monoïde inversif libre est indécidable.)
The theory of abelian p-groups with the quantifier I is decidable
The theory of Archimedean real closed fields in logics with Ramsey quantifiers
The theory of boolean algebras with a distinguished subalgebra is undecidable
The theory of differentially closed fields in logics with cardinal quantifiers.
The Theory of Successor with an Extra Predicate.
The Undecidability of Pseudo Real Closed Fields.
Théorie des modèles pour des anneaux de fonctions entières et des corps de fonctions méromorphes
Theorien abelscher Gruppen mit einem einstelligen Prädikat
Theories of orders on the set of words
It is shown that small fragments of the first-order theory of the subword order, the (partial) lexicographic path ordering on words, the homomorphism preorder, and the infix order are undecidable. This is in contrast to the decidability of the monadic second-order theory of the prefix order [M.O. Rabin, Trans. Amer. Math. Soc., 1969] and of the theory of the total lexicographic path ordering [P. Narendran and M. Rusinowitch, Lect. Notes Artificial Intelligence, 2000] and, in case of the subword...
Theories of orders on the set of words
It is shown that small fragments of the first-order theory of the subword order, the (partial) lexicographic path ordering on words, the homomorphism preorder, and the infix order are undecidable. This is in contrast to the decidability of the monadic second-order theory of the prefix order [M.O. Rabin, Trans. Amer. Math. Soc., 1969] and of the theory of the total lexicographic path ordering [P. Narendran and M. Rusinowitch, Lect. Notes Artificial Intelligence, 2000] and, in case of the ...