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.