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