5 problems

Geometric representation conjecture. The von Neumann example of a continuous geometry admits a geometric representation over an elementary extension of the reals.

Unit-regularity conjecture. If $R$ is $*$-regular and $\overline{L}(R)$ is proatomic with an orthogonal large partial $n$-frame, then $R$ is unit regular. Every representable ring…

Exceptional-frame conjecture. There are subdirectly irreducible coordinatizable MOLs of height at least $3$ not containing an orthogonal large partial $n$-frame.

Orthogonal-frame conjecture. The analogues of Jónsson's results hold for MOLs with orthogonal large partial $n$-frames.

Bruns's conjecture. Every MOL variety not generated by an $MO_\kappa$ contains a projective plane.