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user38200
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Consider a countable transitive model of ZFC $\mathfrak{M}$.

Let $X$ in $\mathfrak{M}$ be some definable set.

Can we define the "type" $p$ of nondefinable elements of $\mathfrak{M}$$X$? (By type I mean the set of formulas satisfied by the nondefinable elements).

Is $p$ principal or not? (By principal I mean whether $p$ has a generator or not).

Consider a countable transitive model of ZFC $\mathfrak{M}$.

Can we define the "type" $p$ of nondefinable elements of $\mathfrak{M}$? (By type I mean the set of formulas satisfied by the nondefinable elements).

Is $p$ principal or not? (By principal I mean whether $p$ has a generator or not).

Consider a countable transitive model of ZFC $\mathfrak{M}$.

Let $X$ in $\mathfrak{M}$ be some definable set.

Can we define the "type" $p$ of nondefinable elements of $X$? (By type I mean the set of formulas satisfied by the nondefinable elements).

Is $p$ principal or not? (By principal I mean whether $p$ has a generator or not).

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user38200
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Consider a ctmcountable transitive model of ZFC $\mathfrak{M}$.

Can we define the "type" $p$ of nondefinable elements of $\mathfrak{M}$? (By type I mean the set of formulas satisfied by the nondefinable elements).

Is $p$ principal or not? (By principal I mean whether $p$ has a generator or not).

Consider a ctm of ZFC $\mathfrak{M}$.

Can we define the "type" $p$ of nondefinable elements of $\mathfrak{M}$?

Is $p$ principal or not?

Consider a countable transitive model of ZFC $\mathfrak{M}$.

Can we define the "type" $p$ of nondefinable elements of $\mathfrak{M}$? (By type I mean the set of formulas satisfied by the nondefinable elements).

Is $p$ principal or not? (By principal I mean whether $p$ has a generator or not).

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user38200
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The type of nondefinable elements

Consider a ctm of ZFC $\mathfrak{M}$.

Can we define the "type" $p$ of nondefinable elements of $\mathfrak{M}$?

Is $p$ principal or not?