# Science Quiz / Set Theory A to Z

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## Can you name these terms from set theory?

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These numbers represent the cardinalities of infinite sets.A
This paradox shows that the axiom of choice allows a single ball to be cut into finitely many pieces and then be rearranged into two balls of equal volume to the first.B
This mathematician is regarded as the founder of set theory.C
The above mathematician used this technique to prove that the real numbers are uncountable.D
This David Foster Wallace book is about set theory.E
Any set bijective to a proper subset of the natural numbers must necessarily have this property.F
This logician showed that the continuum hypothesis cannot be disproven in ZFC. He is better known for his two 'incompleteness theorems.'G
This mathematician included the continuum hypothesis as the first of his namesake problems.H
The symbol for this operation resembles an upside-down U. I
This Penn State set theorist is the author of multiple textbooks on set theory, such as Set Theory and The Axiom of Choice.J
With Platek, this logician and philosopher created an axiom system for set theory weaker than ZFC. He also wrote an analysis of Wittgenstein's Philosophical Investigations.K
This word refers to cardinals which cannot be proven to exist using the axioms of ZFC.L
With ZFC, this axiom implies the continuum hypothesis, though it is independent of ZFC and the negation of the continuum hypothesis. Solvay and its namesake introduced it in 1970.M
Russell's paradox is a paradox in this type of set theory which does not have strict axioms. N
The smallest infinite one of this type of number is denoted with a lowercase omega.O
These axioms of arithmetic can be proven from the ZFC axioms of set theory.P
'For all' and 'there exists' are two of these types of entities in first order logic.Q
This set is denoted with a blackboard bold Q.R
Subsets of a larger set are typically described using this notation. In this notation, a logical predicate is preceded by a vertical bar or a colon. S
The axiom of choice is equivalent to Tychonoff's Theorem, which asserts the compactness of a certain type of this mathematical structure.T
This operation on two sets yields a set containing the elements of both sets.U
This mathematician names a hierarchy of sets constructed using ZFC. He also developed game theory.V
The axiom of choice asserts that one of these constructions exists for every set, though many mathematicians struggle to envision an example over the real numbers.W
This webcomic by Randall Munroe includes multiple jokes about set theory.X
One of the first textbooks on set theory was The Theory of Sets of Points by William and his wife Grace, two mathematicians with this surname.Y
Along with Fraenkel, this man established the axioms of modern set theory.Z

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Created Jul 11, 2017Favorite
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