-
Dummett showed that infinite-valued
propositional Gödel
logic can be
axiomatised by
adding the
axiom schema ( A → B ) ∨ ( B → A ) {\displaystyle (A\rightarrow...
-
seemed more and more plausible, as
large parts of
mathematics became axiomatised and thus
subject to the
simple criteria of
rigorous proof. Pure mathematics...
- \phi } .
These three additional rules extend the
propositional system to
axiomatise classical predicate logic. Likewise,
these three rules extend system for...
-
entailed by GD over
minimal logic. Law of the
excluded middle (LEM),
axiomatised A ∨ ¬ A {\displaystyle A\vee \neg A} , is the most
often cited formulation...
- with sets and
their elements. It is
possible to
start differently, by
axiomatising not
elements of sets but
functions between sets. This can be done by...
-
Zermelo set
theory was
successful precisely because it was
capable of
axiomatising "ordinary" mathematics,
fulfilling the
programme begun by
Cantor over...
- has been work on
classes of
models defined semantically rather than
axiomatised by a
logical theory. One
example is
homogeneous model theory,
which studies...
- Peirce's
existential graphs can be
axiomatised as a
Frobenius algebra, the cuts are
unary operators on
homsets that
axiomatise logical negation. This makes...
- Frege's
first work, the
Begriffsschrift ("concept script") is a
rigorously axiomatised system of
propositional logic,
relying on just two
connectives (negational...
- are
further generalisations of
symplectic manifolds,
which arise by
axiomatising the
properties satisfied by the
Poisson bracket on R 2 n {\displaystyle...
