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The Philosophy of Set Theory

The Philosophy of Set Theory Quiz

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Questions

Question 1 Multiple Choice (Single Answer)

What is the Zermelo-Fraenkel set theory?

  1. A set of axioms used to define the concept of a set
  2. A method for constructing sets
  3. A theory of the relationship between sets and other mathematical objects
  4. A set of rules for manipulating sets
Question 2 Multiple Choice (Single Answer)

What is the axiom of extensionality?

  1. Two sets are equal if and only if they have the same elements
  2. Two sets are equal if and only if they have the same number of elements
  3. Two sets are equal if and only if they are constructed in the same way
  4. Two sets are equal if and only if they are both empty
Question 3 Multiple Choice (Single Answer)

What is the axiom of regularity?

  1. Every set is a member of another set
  2. Every set is a subset of another set
  3. Every set is a proper subset of another set
  4. Every set is a disjoint set
Question 4 Multiple Choice (Single Answer)

What is the axiom of choice?

  1. For any collection of non-empty sets, there exists a function that selects an element from each set
  2. For any collection of non-empty sets, there exists a set that contains exactly one element from each set
  3. For any collection of non-empty sets, there exists a set that contains all of the elements from all of the sets
  4. For any collection of non-empty sets, there exists a set that is disjoint from all of the sets
Question 5 Multiple Choice (Single Answer)

What is the continuum hypothesis?

  1. The cardinality of the set of real numbers is equal to the cardinality of the set of natural numbers
  2. The cardinality of the set of real numbers is equal to the cardinality of the set of integers
  3. The cardinality of the set of real numbers is equal to the cardinality of the set of rational numbers
  4. The cardinality of the set of real numbers is equal to the cardinality of the set of irrational numbers
Question 6 Multiple Choice (Single Answer)

What is the Löwenheim-Skolem theorem?

  1. Any first-order theory that has a model has a model of any infinite cardinality
  2. Any first-order theory that has a model has a model of any finite cardinality
  3. Any first-order theory that has a model has a model of any countable cardinality
  4. Any first-order theory that has a model has a model of any uncountable cardinality
Question 7 Multiple Choice (Single Answer)

What is the Gödel-Bernays set theory?

  1. A set theory that is based on the Zermelo-Fraenkel set theory
  2. A set theory that is based on the von Neumann-Bernays-Gödel set theory
  3. A set theory that is based on the Morse-Kelley set theory
  4. A set theory that is based on the Tarski-Grothendieck set theory
Question 8 Multiple Choice (Single Answer)

What is the von Neumann-Bernays-Gödel set theory?

  1. A set theory that is based on the Zermelo-Fraenkel set theory
  2. A set theory that is based on the Gödel-Bernays set theory
  3. A set theory that is based on the Morse-Kelley set theory
  4. A set theory that is based on the Tarski-Grothendieck set theory
Question 9 Multiple Choice (Single Answer)

What is the Morse-Kelley set theory?

  1. A set theory that is based on the Zermelo-Fraenkel set theory
  2. A set theory that is based on the Gödel-Bernays set theory
  3. A set theory that is based on the von Neumann-Bernays-Gödel set theory
  4. A set theory that is based on the Tarski-Grothendieck set theory
Question 10 Multiple Choice (Single Answer)

What is the Tarski-Grothendieck set theory?

  1. A set theory that is based on the Zermelo-Fraenkel set theory
  2. A set theory that is based on the Gödel-Bernays set theory
  3. A set theory that is based on the von Neumann-Bernays-Gödel set theory
  4. A set theory that is based on the Morse-Kelley set theory
Question 11 Multiple Choice (Single Answer)

What is the Zermelo-Fraenkel-Skolem set theory?

  1. A set theory that is based on the Zermelo-Fraenkel set theory
  2. A set theory that is based on the Gödel-Bernays set theory
  3. A set theory that is based on the von Neumann-Bernays-Gödel set theory
  4. A set theory that is based on the Tarski-Grothendieck set theory
Question 12 Multiple Choice (Single Answer)

What is the New Foundations set theory?

  1. A set theory that is based on the Zermelo-Fraenkel set theory
  2. A set theory that is based on the Gödel-Bernays set theory
  3. A set theory that is based on the von Neumann-Bernays-Gödel set theory
  4. A set theory that is based on the Tarski-Grothendieck set theory
Question 13 Multiple Choice (Single Answer)

What is the Quine set theory?

  1. A set theory that is based on the Zermelo-Fraenkel set theory
  2. A set theory that is based on the Gödel-Bernays set theory
  3. A set theory that is based on the von Neumann-Bernays-Gödel set theory
  4. A set theory that is based on the Tarski-Grothendieck set theory
Question 14 Multiple Choice (Single Answer)

What is the Scott-Potter set theory?

  1. A set theory that is based on the Zermelo-Fraenkel set theory
  2. A set theory that is based on the Gödel-Bernays set theory
  3. A set theory that is based on the von Neumann-Bernays-Gödel set theory
  4. A set theory that is based on the Tarski-Grothendieck set theory
Question 15 Multiple Choice (Single Answer)

What is the Zermelo-Fraenkel-Mostowski set theory?

  1. A set theory that is based on the Zermelo-Fraenkel set theory
  2. A set theory that is based on the Gödel-Bernays set theory
  3. A set theory that is based on the von Neumann-Bernays-Gödel set theory
  4. A set theory that is based on the Tarski-Grothendieck set theory
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