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first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
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The smallest initial ordinal which is not defined using first-order formulas with parameters...
Let $\theta_\alpha$ be the smallest ordinal such that there is no first-order formula $\phi$ such that:
$$\exists\beta_0,\beta_1...\beta_n\in\alpha\forall x(\phi(x,\theta_{\beta_0},\theta_{\beta_1}.. …
3
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0
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Consistency of Nontrivial Elementary Embedding from $\omega_1$ to itself?
I was wondering about a way to make really large countable ordinals. It turns out that in certain models of ZFC (for example pointwise definable ones) every ordinal is definable with no parameters, wh …
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What are some reasonable-sounding statements that are independent of ZFC?
I really think the following one is just intuitive. However, not only is it consistent to be false in ZFC, it is actually not known to be consistent in ZFC (its consistency follows from the existence …