nLab
foundations and logic

Main articles

• Foundations
• Logic
• Philosophy

Axiomatic set theory

Basic axioms and notions

• apartness relation
• axiom of choice, axiom of extensionality, axiom of foundation, axiom of infinity, axiom of multiple choice, axiom of pairing, axiom of replacement, axiom of union
• COSHEP
• ETCS
• Trimble on ETCS: I, II, III
• Grothendieck universe
• internal set
• material set theory
• inhabited set
• pure set
• set theory

Model theory

• model theory
• Mostowski's collapsing lemma
• nonstandard analysis
• forcing
• Skolem's paradox
• Vopěnka's principle

Other

• Boolean algebra
• constructive mathematics
• equality
• evil
• Heyting algebra
• infinity-topos
• internal logic
• intuitionism
• linear logic
• predicative mathematics
• theory
• truth value
• type theory