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Frode Alfson Bjørdal
Frode Alfson Bjørdal
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Countable $L\alpha$$L_\alpha$ model for $S$ if $S$ has a countable well founded model?

Let $S$ be a proper fragment of $\mathit{ZFC}$, and let $S$ properly extend $\mathit{ZFC}^-$, i.e. $\mathit{ZFC}$ minus the power set axiom. Is there a countable ordinal $\alpha$ so that $L\alpha$$L_\alpha$ is a model of $S$ if $S$ has a countable well founded model?

Countable $L\alpha$ model for $S$ if $S$ has a countable well founded model?

Let $S$ be a proper fragment of $\mathit{ZFC}$, and let $S$ properly extend $\mathit{ZFC}^-$, i.e. $\mathit{ZFC}$ minus the power set axiom. Is there a countable ordinal $\alpha$ so that $L\alpha$ is a model of $S$ if $S$ has a countable well founded model?

Countable $L_\alpha$ model for $S$ if $S$ has a countable well founded model?

Let $S$ be a proper fragment of $\mathit{ZFC}$, and let $S$ properly extend $\mathit{ZFC}^-$, i.e. $\mathit{ZFC}$ minus the power set axiom. Is there a countable ordinal $\alpha$ so that $L_\alpha$ is a model of $S$ if $S$ has a countable well founded model?

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LSpice
LSpice
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Let S$S$ be a proper fragment of $ZFC$$\mathit{ZFC}$, and let S$S$ properly extend $ZFC^-$$\mathit{ZFC}^-$, i.e. $ZFC$$\mathit{ZFC}$ minus the power set axiom. Is there a countable ordinal $\alpha$ so that $L\alpha$ is a model of S$S$ if S$S$ has a countable well founded model?

Let S be a proper fragment of $ZFC$, and let S properly extend $ZFC^-$, i.e. $ZFC$ minus the power set axiom. Is there a countable ordinal $\alpha$ so that $L\alpha$ is a model of S if S has a countable well founded model?

Let $S$ be a proper fragment of $\mathit{ZFC}$, and let $S$ properly extend $\mathit{ZFC}^-$, i.e. $\mathit{ZFC}$ minus the power set axiom. Is there a countable ordinal $\alpha$ so that $L\alpha$ is a model of $S$ if $S$ has a countable well founded model?

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

Countable $L\alpha$ model for $S$ if $S$ has a countable well founded model?

Let S be a proper fragment of $ZFC$, and let S properly extend $ZFC^-$, i.e. $ZFC$ minus the power set axiom. Is there a countable ordinal $\alpha$ so that $L\alpha$ is a model of S if S has a countable well founded model?