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Results tagged with lo.logic
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user 140821
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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PAC and totally real fields
A field $K$ is called pseudo-algebraically closed (PAC) if every absolutely irreducible variety over $K$ has a $K$-point. Let $L$ be the maximal totally real subfield of $\overline{\mathbb Q}$. A few …
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1
vote
Is this theory the complete theory of the real ordered field?
EDIT 2: This wrong proof at least shows that the upper bound property holds in $K(\pi)$, when $\phi$ is $\Sigma_1$. Indeed, if $\phi$ is $\Sigma_1$ then we have the inclusion of solution sets
$$ \phi( …
- 584