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Results tagged with lo.logic
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user 1631
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.
8
votes
Clearing misconceptions: Defining "is a model of ZFC" in ZFC
I suspect these sorts of problems arise in two ways: ignoring wrongness (e.g. Skolem's paradox, that there are countable models of set theory which believe in uncountable sets) and ignoring first-orde …
- 1,987
1
vote
Name for "lower/upper bounds" of arbitrary relations?
In a pre-order $\prec$ (or a category) one can speak of initial objects $0$, or terminal objects $1$, meaning that $0\prec x$ for all $x$ --- (or $0\rightarrow^! x$ ) --- which also gives the notion o …
- 1,987
1
vote
Are all mathematical theorems necessarily true?
As I understand the word "tautology" from Mathematical Logic; a logic $L$ means a formal system of deductions $\Sigma \vdash_L \Phi$, satisfying some rules, where $\Sigma$ is a set of propositions and …
- 1,987
0
votes
Where does the generic triangle live?
As it happens, the klein hyperbolic models, the usual euclidean plane, and central projection for projective space all have geodesics that look like straight lines; on the other hand, these maps can't …
- 1,987