Mathematics Problem Archive

Determine the automorphism group of the partial order of Turing degrees....

The main gap conjecture, e.g. for uncountable first order theories, for AECs, and for $\aleph_1$-saturated models of a countable theory....

Shelah's categoricity conjecture for $L_{\omega_1,\omega}$: If a sentence is categorical above the Hanf number then it is categorical in all cardinals...

Shelah's eventual categoricity conjecture: For every cardinal $\lambda$ there exists a cardinal $\mu(\lambda)$ such that if an AEC K with LS(K)${} \le...

Does every simple first-order theory have stable forking?...

The universality problem for C-free graphs: For which finite sets C of graphs does the class of C-free countable graphs have a universal member under ...

Assume K is the class of models of a countable first order theory omitting countably many types. If K has a model of cardinality $\aleph_{\omega_1}$ d...

If the class of atomic models of a complete first order theory is categorical in the $\aleph_n$, is it categorical in every cardinal?...

Is the Borel monadic theory of the real order (BMTO) decidable? Is the monadic theory of well-ordering (MTWO) consistently decidable?...