axiom system

C17826 concept

An axiom system is a structured set of foundational statements or principles from which theorems and further truths within a formal theory are logically derived.

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Observed surface forms (17)

logical system ×5
deductive system ×3
concept in automated theorem proving ×2
axiom of ordered fields ×1
axiom of set theory ×1
axiomatic formulation ×1
axiomatic proof system ×1
axiomatic theory ×1
formal proof system ×1
foundational assumptions of Euclidean geometry ×1

Instances (20)

Russellian logic via concept surface "logical system"
Blum axioms
Carathéodory’s formulation of the second law of thermodynamics via concept surface "axiomatic formulation"
Archimedean property of real numbers via concept surface "axiom of ordered fields"
Herbrand universe via concept surface "concept in automated theorem proving"
Leibnizian logic via concept surface "logical system"
Veblen axioms for projective geometry
Kleene strong three-valued logic via concept surface "logical system"
Buddhist logic via concept surface "logical system"
Hilbert-style deductive systems via concept surface "deductive system"
Axiom of Extensionality in set theory via concept surface "axiom of set theory"
surface form: Axiom of Extensionality
Atiyah–Segal axioms via concept surface "set of mathematical axioms"
Playfair's axiom via concept surface "geometric axiom"
Euclid's postulates via concept surface "geometric axiom set"
Eilenberg–Steenrod axioms via concept surface "set of axioms"
Callen formulation of thermodynamics via concept surface "axiomatic theory"
Herbrand base via concept surface "concept in automated theorem proving"
sequent calculus via concept surface "deductive system"
Gentzen-style proof systems via concept surface "deductive system"
predicate logic via concept surface "logical system"