In constructive set theory, where the law of excluded middle does not necessarily hold, one can consider the relation'subquotient of'as replacing the usual order relation ( s ) on cardinals.
42.
Because of the change in designated values relative to the WHERE clause, from a logic perspective the law of excluded middle is a tautology for CHECK constraints, meaning CHECK ( " p"
43.
:Bishop's preoccupation with the extirpation of the law of excluded middle led him to criticize classical mathematics as a whole in as vitriolic a manner as his criticism of non-standard analysis.
44.
Where someone questions the law of excluded middle " in-world "-- does that mean that possibly there ARE no actual truth statements in the world ? ( In a binary sense ).
45.
In constructive set theory, however, Diaconescu's theorem shows that the axiom of choice implies the law of excluded middle ( unlike in Martin-L�f type theory, where it does not ).
46.
Certain resolutions of these paradoxes, particularly Graham Priest's dialetheism as formalised in LP, have the law of excluded middle as a theorem, but resolve out the Liar as both true and false.
47.
The principle of bivalence is related to the law of excluded middle though the latter is a syntactic expression of the language of a logic of the form " P ( " & not; P ".
48.
On the other hand, the law of excluded middle P \ vee ( \ neg P ) expands to P \ vee ( P \ to \ bot ), and in general has no proof.
49.
It is characterized by rejecting the law of excluded middle : as a consequence it does not in general accept rules such as double negation elimination and the use of reductio ad absurdum to prove the existence of something.
50.
The initials " RCA " stand for " recursive comprehension axiom ", where " recursive " means " computable ", as in constructivism because it is a theory in classical logic including the law of excluded middle.
