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