Nicely done. I should have spent more time thinking about liar sentences; you really can do a lot with them.

Follow-up question—is the set of limits of logical inductors convex? (Your proof also makes me curious as to whether the set of “expanded limits” {liminfn→∞Pn(ϕn)}¯¯¯ϕ efficiently computable is convex, though that question is a bit less nice than the other).

From conversation with Scott and Michael Dennis: there aren’t enough logical inductors to make the set of limits convex, since there are an uncountable number of convex combinations but only a countable number of inductors (and thus limits). The interesting question would be whether any rational/computable convex combination of limits of logical inductors is a logical inductor.

Nicely done. I should have spent more time thinking about liar sentences; you really can do a lot with them.

Follow-up question—is the set of limits of logical inductors convex? (Your proof also makes me curious as to whether the set of “expanded limits” {liminfn→∞Pn(ϕn)}¯¯¯ϕ efficiently computable is convex, though that question is a bit less nice than the other).

From conversation with Scott and Michael Dennis: there aren’t enough logical inductors to make the set of limits convex, since there are an uncountable number of convex combinations but only a countable number of inductors (and thus limits). The interesting question would be whether any rational/computable convex combination of limits of logical inductors is a logical inductor.