-
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...
-
seemed more and more plausible, as
large parts of
mathematics became axiomatised and thus
subject to the
simple criteria of
rigorous proof. Pure mathematics...
-
Dummett showed that infinite-valued
propositional Gödel
logic can be
axiomatised by
adding the
axiom schema ( A → B ) ∨ ( B → A ) {\displaystyle (A\rightarrow...
- K
consists exactly of the
reducts to σ of σ'-structures in K'. K' is
axiomatised by the
single sentence ( ∀ x ∀ y ( f ( x ) = f ( y ) → x = y ) ∧ ∃ y...
- 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...
- many theories,
including Peano arithmetic,
which cannot be
properly axiomatised in
finitary logic, can be in a
suitable infinitary logic.
Other examples...
- for over 30 years. However, in the 1960s
through 1980s the
method was
axiomatised and
applied in a
variety of
types of study.
Choice modelling is used...
-
Zermelo set
theory was
successful precisely because it was
capable of
axiomatising "ordinary" mathematics,
fulfilling the
programme begun by
Cantor over...
- that one of
these fields exists for each
uncountable cardinality. He
axiomatised these fields and,
using Hrushovski's
construction and
techniques inspired...
-
topos theory. A
theory of first-order
logic is
geometric if it is can be
axiomatised using only
axioms of the form ⋀ i ∈ I ϕ i , 1 ∨ ⋯ ∨ ϕ i , n i ⟹ ⋁ j ∈...
