-
derivation of x ∨ (y ∧ z) = x ∨ (z ∧ y) from y ∧ z = z ∧ y (as
treated in §
Axiomatizing Boolean algebra).
Boolean algebra satisfies many of the same laws as...
- In 1936,
Alfred Tarski gave an
axiomatization of the real
numbers and
their arithmetic,
consisting of only the
eight axioms shown below and a mere four...
-
there are
certain consistent bodies of
propositions with no
recursive axiomatization. Typically, the
computer can
recognize the
axioms and
logical rules...
- the
standard ZFC
axiomatization of set theory. Czesław Ryll-Nardzewski
proved that
Peano arithmetic cannot be
finitely axiomatized, and
Richard Montague...
-
impossible to
axiomatize ZFC
using only
finitely many axioms. On the
other hand, von Neumann–Bernays–Gödel set
theory (NBG) can be
finitely axiomatized. The ontology...
-
Sanders Peirce provided an
axiomatization of natural-number arithmetic. In 1888,
Richard Dedekind proposed another axiomatization of natural-number arithmetic...
-
arithmetic of the
natural numbers and
which are
consistent and
effectively axiomatized.
Particularly in the
context of first-order logic,
formal systems are...
- (compact
totally disconnected Hausdorff)
topological space. The
first axiomatization of
Boolean lattices/algebras in
general was
given by the
English philosopher...
-
negation (¬),
implication (→) and
propositional symbols. A well-known
axiomatization,
comprising three axiom schemata and one
inference rule (modus ponens)...
- self-evident in
nature (e.g., the
parallel postulate in
Euclidean geometry). To
axiomatize a
system of
knowledge is to show that its
claims can be
derived from a...
