In this paper of Foreman, there are some problems with interesting reward formulae.

Question(Steel) Working in $\rm ZFC$, either
(a) show that if $\rm ZFC$ plus “there is a singular strong limit $\kappa$ such that $\neg \square_\kappa$” is consistent, then so is $\rm ZFC$ plus “there is a superstrong cardinal”, or
(b) show that if there is a superstrong cardinal, then $\rm ZFC$ plus “there is a singular strong limit κ such that $\neg \square_\kappa$” is consistent.

Reward: For (b), $\\\$300$. For (a), $\\\$4000−500x$, where $x$ is the time in years from May 1, 2004 to the submission of a manuscript with a correct, complete proof. UC Berkeley faculty are not eligible for the reward!

Question (Woodin) Suppose that there is an extendible cardinal. Must $\rm HOD$ compute the successor correctly for some (uncountable) cardinal?

Prize: $$\\\$1000\times[{\rm max(min}(n, 10 − n), 1)]$$ where $$n = (\text{calender year of submission}) − 2004$$.
Terms: Collect if a correct proof is given for either “yes”, or if a correct proof is given that the failure implies the consistency with $\rm ZFC$ of the large cardinal $I0$ of Kanamori’s book. (Details: Clay rules)

In this paper of Foreman, there are some problems with interesting reward formulae.

Question(Steel) Working in $\rm ZFC$, either
(a) show that if $\rm ZFC$ plus “there is a singular strong limit $\kappa$ such that $\neg \square_\kappa$” is consistent, then so is $\rm ZFC$ plus “there is a superstrong cardinal”, or
(b) show that if there is a superstrong cardinal, then $\rm ZFC$ plus “there is a singular strong limit κ such that $\neg \square_\kappa$” is consistent.

Reward: For (b), $\\\$300$. For (a), $\\\$4000−500x$, where $x$ is the time in years from May 1, 2004 to the submission of a manuscript with a correct, complete proof. UC Berkeley faculty are not eligible for the reward!

Question (Woodin) Suppose that there is an extendible cardinal. Must $\rm HOD$ compute the successor correctly for some (uncountable) cardinal?

Prize: $$\\\$1000\times[{\rm max(min}(n, 10 − n), 1)]$$ where $$n = (\text{calender year of submission}) − 2004$$.
Terms: Collect if a correct proof is given for either “yes”, or if a correct proof is given that the failure implies the consistency with $\rm ZFC$ of the large cardinal $I0$ of Kanamori’s book. (Details: Clay rules)

In this paper of Foreman, there are some problems with interesting reward formulae.

Question(Steel) Working in $\rm ZFC$, either
(a) show that if $\rm ZFC$ plus “there is a singular strong limit $\kappa$ such that $\neg \square_\kappa$” is consistent, then so is $\rm ZFC$ plus “there is a superstrong cardinal”, or
(b) show that if there is a superstrong cardinal, then $\rm ZFC$ plus “there is a singular strong limit κ such that $\neg \square_\kappa$” is consistent.

Reward: For (b), $\\\$300$. For (a), $\\\$4000−500x$, where $x$ is the time in years from May 1, 2004 to the submission of a manuscript with a correct, complete proof. UC Berkeley faculty are not eligible for the reward!

Question (Woodin) Suppose that there is an extendible cardinal. Must $\rm HOD$ compute the successor correctly for some (uncountable) cardinal?

Prize: $\\\$1000\times[{\rm max(min}(n, 10 − n), 1)]$ where $n = (\text{calender year of submission}) − 2004$.
Terms: Collect if a correct proof is given for either “yes”, or if a correct proof is given that the failure implies the consistency with $\rm ZFC$ of the large cardinal $I0$ of Kanamori’s book. (Details: Clay rules)

In this paper of Foreman, there are some problems with interesting reward formulae.

Question(Steel) Working in $\rm ZFC$, either
(a) show that if $\rm ZFC$ plus “there is a singular strong limit $\kappa$ such that $\neg \square_\kappa$” is consistent, then so is $\rm ZFC$ plus “there is a superstrong cardinal”, or
(b) show that if there is a superstrong cardinal, then $\rm ZFC$ plus “there is a singular strong limit κ such that $\neg \square_\kappa$” is consistent.

Reward: For (b), $\\\$300$. For (a), $\\\$4000−500x$, where $x$ is the time in years from May 1, 2004 to the submission of a manuscript with a correct, complete proof. UC Berkeley faculty are not eligible for the reward!

Question (Woodin) Suppose that there is an extendible cardinal. Must $\rm HOD$ compute the successor correctly for some (uncountable) cardinal?

Prize: $$\\\$1000\times[{\rm max(min}(n, 10 − n), 1)]$$ where $$n = (\text{calender year of submission}) − 2004$$.
Terms: Collect if a correct proof is given for either “yes”, or if a correct proof is given that the failure implies the consistency with $\rm ZFC$ of the large cardinal $I0$ of Kanamori’s book. (Details: Clay rules)