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