axiomatic set theory

C4422

concept

Axiomatic set theory is a branch of mathematical logic that studies sets and their relationships by formulating precise axioms to avoid paradoxes and provide a rigorous foundation for mathematics.

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All labels observed (12)

Label	Occurrences
axiomatic set theory canonical	7
first-order theory	3
set theory	3
class model of set theory	1
conservative extension of Zermelo–Fraenkel set theory	1
formalization of set theory	1
second-order set theory	1
set theory axiom	1
set-theoretic axiom	1
subsystem of Zermelo–Fraenkel set theory	1
two-sorted first-order theory	1
work in set theory	1

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: axiomatic set theory

Generated description

Axiomatic set theory is a branch of mathematical logic that studies sets and their relationships by formulating precise axioms to avoid paradoxes and provide a rigorous foundation for mathematics.

Instances (15)

Instance	Via concept surface
constructible universe	class model of set theory
Zermelo–Fraenkel set theory	—
von Neumann–Bernays–Gödel set theory	—
Peano arithmetic	first-order theory
naive set theory	set theory
Kripke–Platek set theory	set theory
Fraenkel surface form: Zermelo–Fraenkel set theory	—
Gödel 1940 monograph "The Consistency of the Continuum Hypothesis" surface form: The Consistency of the Continuum Hypothesis	work in set theory
Isabelle/ZF	formalization of set theory
ZF	—
axiom schema of separation	set theory axiom
Skolem arithmetic	first-order theory
Zermelo set theory	—
axiom of choice	set-theoretic axiom
Morse–Kelley set theory by class–set distinction	—