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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All labels observed (18)

Label Occurrences
logical system 5
deductive system 3
axiom system canonical 2

Description generation (CDg)

The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.

Instruction
generate a one-sentence description for a given conceptual class.
# Response Format
Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: axiom system
Generated description
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.

Instances (20)

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