A nonstandard approach to arithmetic.
Degrees of interpretability
Die Nichtaxiomatisierbarkeit der unendlichwertigen Mengenlehre.
Die Unentscheidbarkeit der einstelligen unendlichwertigen Prädikatenlogik.
Different levels of word problems for some varieties.
Diophantine Undecidability of Holomorphy Rings of Function Fields of Characteristic 0
Let be a one-variable function field over a field of constants of characteristic 0. Let be a holomorphy subring of , not equal to . We prove the following undecidability results for : if is recursive, then Hilbert’s Tenth Problem is undecidable in . In general, there exist such that there is no algorithm to tell whether a polynomial equation with coefficients in has solutions in .
Disconnectedness of Sublevel Sets of Some Riemannian.
Existential interpretation. II.
Groups of automatic automorphisms of some automatic structures.
Highly Undecidable Problems For Infinite Computations
We show that many classical decision problems about 1-counter ω-languages, context free ω-languages, or infinitary rational relations, are Π½ -complete, hence located at the second level of the analytical hierarchy, and “highly undecidable”. In particular, the universality problem, the inclusion problem, the equivalence problem, the determinizability problem, the complementability problem, and the unambiguity problem are all Π½ -complete for context-free ω-languages or for infinitary rational...
Metamathematical discussion of some affine geometries
Model-theoretic properties of cause-and-effect structures
On a connection between the word problem and decidability of the equational theory.
Partial conservativity revisited
Recursive inseparability of the sets of identically valid and finitely refutable formulas of some elementary theories of varieties.
Some diophantine forms of Gödel's theorem.
Some undecidable theories with monadic predicates and without equality.
The computability potential scale of all finite algebras.
The connection between the fundamental groupoid and a unification algorithm for syntactil algebras (extended abstract)
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...