A) Axioms 1–7 B) Axioms 1–9 C) Axioms 2–9 D) Axioms 1–8
A) The well-ordering theorem B) The axiom of infinity C) The axiom of extensionality D) The axiom of regularity
A) The axiom of extensionality implies it B) The axiom of specification implies it C) It is a theorem of first-order logic that something exists D) It is assumed that the domain of discourse is empty
A) It only exists in the axiom of pairing B) In free logic where first-order logic does not prove existence C) It is never guaranteed by the axiom of infinity D) It is only guaranteed if the domain is finite
A) Every set has a unique subset B) No set is an element of itself C) Two sets are equal if they have the same rank D) Two sets are equal if they have the same elements
A) The axiom of specification B) The axiom of substitution C) The axiom of union D) The axiom of foundation
A) It contains an empty set B) It contains a member disjoint from itself C) It is an element of itself D) It must be infinite
A) There exists an empty set B) Every set is unique C) All sets are finite D) No set is an element of itself
A) Axiom of infinity or union B) Axiom of separation or restricted comprehension C) Axiom of identity or equality D) Axiom of choice or foundation
A) Because sets cannot contain other sets B) To avoid Russell's paradox C) To increase the speed of proofs D) To force the existence of the empty set
A) Russell's paradox B) The existence of an ordinal rank C) The well-ordering theorem D) The uniqueness of the empty set
A) By using a property that no set has B) By the axiom of regularity C) By the axiom of extensionality D) By the axiom of infinity
A) It contains itself B) It is unique C) It depends on the set w D) It does not exist
A) The empty set does not exist B) Russell's paradox is resolved C) Every set has an ordinal rank D) The axiom of choice is unnecessary
A) Ernst Zermelo and Abraham Fraenkel B) Georg Cantor and Gottlob Frege C) Kurt Gödel and John von Neumann D) Bertrand Russell and Paul Bernays
A) The Russellian hierarchy B) The Fraenkel universe C) The Zermelo collection D) The von Neumann universe
A) aleph-null B) aleph-one C) aleph-omega D) aleph-zero
A) As a non-logical predicate B) As a set operator C) As a primitive logical symbol D) As a quantifier
A) A binary relation B) An equality relation C) A unary relation D) A ternary relation
A) An uncountable number B) Zero C) A finite number D) A countably infinite number
A) x ∧ y B) ¬x C) ∀xϕ D) x = y
A) Only one B) Finitely many C) Uncountably infinitely many D) Countably infinitely many
A) I_in B) psi C) mu D) phi
A) Membership relation B) Truth value function C) Domain interpretation function D) Variable assignment function
A) S is a subset of phi B) S satisfies phi C) S is equivalent to phi D) S contains phi
A) Any wff B) Any constant C) Any domain element D) Any variable
A) The set of relations B) A C) D D) The set of wffs
A) S assigns phi to the domain B) S makes phi true C) phi is a member of D D) phi is the interpretation of S
A) φ B) B C) w1 D) A
A) A B) y C) B D) x |