Some problems I have solved

Are all almost everywhere dominating degrees array non-computable?
Problem 8.6.4 in the book by Nies. Solution

What is the arithmetical complexity of the number of K-trivial sets?
Problem 5.2.16 in the book by Nies. and a Section 10.1.4 of the book by Downey & Hirschfeldt. Solution.

Does van Lambalgen's theorem hold for weak 2-randomness?
Problem 3.6.9 in the book by Nies. Solution.

Are all weakly 2-random sets array computable?
Problem 8.2.14 in the book by Nies. Solution.

In the LR degrees, can the degree of a weakly 2-random set be below $\mathbf{0}'$?
Problem 5.6.16 in the book by Nies. Solution.

Are the low for Omega LK degrees exactly the ones with countably many predecessors?
Problem 8.1.13 in the book by Nies. and in J. S. Miller. Notre Dame J. Formal Logic (2010). Solution.

Can an almost everywhere dominating function have minimal Turing degree?
A question of Simpson. Solution.

Is there a proper prime $\Sigma^0_4$ ideal in the c.e. degrees?
A question of Calhoun in Incomparable prime ideals of r.e. degrees. Ann. Pure Appl. Logic, (1993). Solution.

What is the measure of the Turing degrees which satisfy the cupping property?
A question of Jockusch. Solution.

Are there c.e. reals that form a minimal pair in the $K$-degrees?
A question in the book. Solution by Downey & Hirschfeldt.

Is there a c.e. exact pair for the ideal of the K-trivial degrees?
Question 4.2 in the BSL survey by Miller and Nies, and Problem 5.5.8 in Nies' book.
Solution