Questions tagged [infinitary-sentences]
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3 questions
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On undefinability of well-orderings in $L_{\omega_1,\omega}$
It is a well-known theorem that well-orderings can not be characterized in $L_{\omega_1,\omega}$.
In particular, if $\psi$ is an $L_{\omega_1,\omega}$-sentence in a vocabulary $\tau$ that contains a ...
- 2,882
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Does Keisler-Shelah isomorphism theorem hold for infinitary logics?
In model theory, the Keisler-Shelah isomorphism theorem asserts that two models of a theory are elementary equivalent if and only if they have isomorphic ultrapowers. On the other hand, assuming that $...
- 5,902
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Example with right-open amalgamation spectrum
Let $\phi$ be an $L_{\omega_1,\omega}$ sentence. The amalgamation spectrum of $\phi$ is the set of all cardinals $\kappa$ such that the models of $\phi$ of size $\kappa$ satisfy amalgamation.
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