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Results tagged with lo.logic
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user 24864
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.
1
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Proof " A la Grothendieck" [closed]
Grothendieck's proof of the well-known Ax–Grothendieck Theorem uses the elegant argument that the existence of a counterexample for the field $\mathbb C$ imply the existence of a counterexample for a …
- 801
8
votes
3
answers
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Formulas in a Field and in a Field Extension
Let $\mathbb F$ be a field and let $a, b, c, d$ be fixed elements in the field $\mathbb F$.
Consider the formulas
1) $\exists\;x\;\;:\;\;x^2=-1.$
2) $\exists\;x\;\;:\;\;(xa=c\land xb=d).$
Formula …
- 801