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Results tagged with lo.logic
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user 28104
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.
12
votes
Taking a theorem as a definition and proving the original definition as a theorem
A very basic example is the field $\mathbb{C}$ of complex numbers. -- It can be defined as the field one obtains when adjoining the square root of -1 to $\mathbb{R}$, in which case it needs to be prov …
12
votes
About the proof of the proposition "there exists irrational numbers a, b such that a^b is ra...
The proposition can also be proved without explicitly knowing any particular irrational number:
Fix a positive rational number $c$. Then for any positive irrational real number number $a$,
the equati …
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