General set theory - Quiz
  • 1. What kind of statement is the Specification axiom in GST?
A) A finitely axiomatizable theorem
B) A primitive constant
C) A null hypothesis
D) An axiom schema
  • 2. Is GST finitely axiomatizable?
A) Only under specific conditions
B) Yes
C) No
D) It is an unproven conjecture
  • 3. Who demonstrated that ZFC is not finitely axiomatizable?
A) Tarski
B) Montague
C) Russell
D) Givant
  • 4. Which set theory's non-finite axiomatizability argument carries over to GST?
A) Relation algebra
B) ZFC
C) Naïve set theory
D) Cantor's set theory
  • 5. What must any axiomatization of GST include to be valid?
A) A finite set of constant axioms
B) At least one axiom schema
C) More than three quantifiers
D) A proof of Russell's paradox
  • 6. Which of the following is NOT an antinomy that GST is immune to?
A) Tarski's antinomy
B) Russell's antinomy
C) Cantor's antinomy
D) Burali-Forti's antinomy
  • 7. GST is interpretable in which mathematical field?
A) Topology
B) Number theory
C) Relation algebra
D) Calculus
  • 8. What is the maximum number of quantifiers allowed for GST to be interpretable in relation algebra?
A) Two
B) Four
C) Zero
D) Three
  • 9. Who provided the necessary and sufficient condition for GST to be interpretable in relation algebra?
A) Burali and Forti
B) Montague
C) Russell and Cantor
D) Tarski and Givant
  • 10. Who coined the name 'General set theory' (GST)?
A) Bertrand Russell
B) Zermelo
C) Peano
D) George Boolos
  • 11. What is the relationship between GST and Z?
A) GST is the same as Z
B) GST is a fragment of Z
C) Z is a fragment of GST
D) They are unrelated
  • 12. What is the scope of mathematics that GST is sufficient for?
A) All mathematics including infinite sets
B) All mathematics not requiring infinite sets
C) Only geometry
D) Only arithmetic
  • 13. Which axioms are included in the theorems of GST?
A) Second-order Peano axioms
B) First-order Peano axioms
C) Axiom of Choice
D) Axiom of Foundation
  • 14. What does GST assume about individuals in the universe of discourse?
A) They are a mix of sets and atoms
B) They are all urelements
C) They are all sets
D) They are all numbers
  • 15. What is the single primitive binary relation in GST?
A) Function application
B) Set membership
C) Subset relation
D) Equality
  • 16. What is the background logic for GST?
A) First-order logic with identity
B) Intuitionistic logic
C) Propositional logic
D) Second-order logic
  • 17. Which axiom is taken from Z and used as an axiom in GST?
A) Infinity
B) Union
C) Adjunction
D) Power Set
  • 18. What does the Axiom of Extensionality state?
A) Sets with the same members are the same set
B) All sets are equal
C) Sets are composed of individuals
D) The empty set has no members
  • 19. What is another name for the Axiom Schema of Specification?
A) Separation
B) Extensionality
C) Adjunction
D) Foundation
  • 20. Why is the restriction to z necessary in the Axiom Schema of Specification?
A) To satisfy Peano axioms
B) To avoid Russell's paradox
C) To allow for infinite sets
D) To define the empty set
  • 21. Which of these is NOT omitted when deriving GST from Z?
A) Union
B) Extensionality
C) Infinity
D) Power Set
  • 22. Who referred to GST as STZ in their 2005 publication?
A) Givant
B) Burgess
C) Tarski
D) Boolos
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