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

Hint

Answer

Letter

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.

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