Skip to main content
MathOverflow

Return to Question

edited body
Source Link
Zuhair Al-Johar
Zuhair Al-Johar
  • 11.4k
  • 1
  • 13
  • 47

ifIf we say that an effectively generated first order theory $\sf T$ extends $\sf ZF$, such that every countable model of $\sf T$ doesn't have a class forcing extension that is pointwise definable. Would that just mean that $\sf T$ negates Choice? Or it does impart $\sf T$ proving some large cardinal property?

if we say that an effectively generated first order theory $\sf T$ extends $\sf ZF$, such that every countable model of $\sf T$ doesn't have a forcing extension that is pointwise definable. Would that just mean that $\sf T$ negates Choice? Or it does impart $\sf T$ proving some large cardinal property?

If we say that an effectively generated first order theory $\sf T$ extends $\sf ZF$, such that every countable model of $\sf T$ doesn't have a class forcing extension that is pointwise definable. Would that just mean that $\sf T$ negates Choice? Or it does impart $\sf T$ proving some large cardinal property?

Source Link
Zuhair Al-Johar
Zuhair Al-Johar
  • 11.4k
  • 1
  • 13
  • 47

If a theory speaks of sets that cannot be forced to be parameter free definable, then does this entail a large cardinal property?

if we say that an effectively generated first order theory $\sf T$ extends $\sf ZF$, such that every countable model of $\sf T$ doesn't have a forcing extension that is pointwise definable. Would that just mean that $\sf T$ negates Choice? Or it does impart $\sf T$ proving some large cardinal property?