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Results tagged with lo.logic
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user 8494
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.
11
votes
Is all ordinary mathematics contained in high school mathematics?
Since Ackermann's function is not available in EFA, Tarjan's upper bound – the inverse Ackermann function – for the run-time of the union-find data structure is not provable in EFA. This probably does …
- 1,347
0
votes
Construction of a maximal ideal
As Ashutosh points out, it's impossible to describe $M$ constructively.
However, from a practical point view, the "untouchability" of ultrafilters and maximal ideals in $\mathcal C(\mathbb R)$is not …
- 1,347
4
votes
An ultrafilter is a set of subsets containing exactly one element of each finite partition: ...
The alternate formulation is closely related to the following fundamental definition from Ramsey Theory
Definition: Let $\phi : 2^X \to \lbrace\text{true},\text{false}\rbrace$ be a property pertainin …
- 1,347