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Frode Alfson Bjørdal
Frode Alfson Bjørdal
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Kripke Platek set theory has collection instead of replacement, and it is a weakening of KP if one has replacement instead of collection. Call KP minus colectioncollection plus replacement KF for Kripke Fraenkel. Is KF weaker than KP in that some transfinite recursion can be done by KP which cannot be done by KF? If so, is that a difference inherited by strengthened theories as $\Sigma _{n} KP$ and $\Sigma _{n} KF$ for $n>1$?

Kripke Platek set theory has collection instead of replacement, and it is a weakening of KP if one has replacement instead of collection. Call KP minus colection plus replacement KF for Kripke Fraenkel. Is KF weaker than KP in that some transfinite recursion can be done by KP which cannot be done by KF? If so, is that a difference inherited by strengthened theories as $\Sigma _{n} KP$ and $\Sigma _{n} KF$ for $n>1$?

Kripke Platek set theory has collection instead of replacement, and it is a weakening of KP if one has replacement instead of collection. Call KP minus collection plus replacement KF for Kripke Fraenkel. Is KF weaker than KP in that some transfinite recursion can be done by KP which cannot be done by KF? If so, is that a difference inherited by strengthened theories as $\Sigma _{n} KP$ and $\Sigma _{n} KF$ for $n>1$?

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Frode Alfson Bjørdal
Frode Alfson Bjørdal
  • 3.6k
  • 1
  • 15
  • 35

Transfinite recursion, collection and replacement in KP and KF

Kripke Platek set theory has collection instead of replacement, and it is a weakening of KP if one has replacement instead of collection. Call KP minus colection plus replacement KF for Kripke Fraenkel. Is KF weaker than KP in that some transfinite recursion can be done by KP which cannot be done by KF? If so, is that a difference inherited by strengthened theories as $\Sigma _{n} KP$ and $\Sigma _{n} KF$ for $n>1$?