A hierarchy of sets that are defined using transfinite induction

A hierarchy of sets that are defined using the axiom of choice

A hierarchy of sets that are defined using the continuum hypothesis

A hierarchy of sets that are defined using the well-ordering theorem

An analytic set is a set that can be defined using a formula in the language of set theory, while a coanalytic set is a set that can be defined using a formula in the language of set theory with the addition of the axiom of choice

An analytic set is a set that can be defined using a formula in the language of set theory, while a coanalytic set is a set that can be defined using a formula in the language of set theory with the addition of the continuum hypothesis

An analytic set is a set that can be defined using a formula in the language of set theory, while a coanalytic set is a set that can be defined using a formula in the language of set theory with the addition of the well-ordering theorem

An analytic set is a set that can be defined using a formula in the language of set theory, while a coanalytic set is a set that can be defined using a formula in the language of set theory with the addition of the axiom of determinacy

A theorem that states that every analytic set can be separated from every coanalytic set by a Borel set

A theorem that states that every analytic set can be separated from every coanalytic set by a projective set

A theorem that states that every analytic set can be separated from every coanalytic set by a Suslin set

A theorem that states that every analytic set can be separated from every coanalytic set by a Lebesgue measurable set

A theorem that states that every complete metric space is a Baire space

A theorem that states that every complete metric space is a Polish space

A theorem that states that every complete metric space is a Suslin space

A theorem that states that every complete metric space is a Lebesgue measurable space

A theorem that states that every non-empty perfect set in a complete metric space is uncountable

A theorem that states that every non-empty perfect set in a complete metric space is Lebesgue measurable

A theorem that states that every non-empty perfect set in a complete metric space is a Baire space

A theorem that states that every non-empty perfect set in a complete metric space is a Polish space

A theorem that states that every set of real numbers can be decomposed into a perfect set and a countable set

A theorem that states that every set of real numbers can be decomposed into a perfect set and a Lebesgue measurable set

A theorem that states that every set of real numbers can be decomposed into a perfect set and a Baire space

A theorem that states that every set of real numbers can be decomposed into a perfect set and a Polish space

A theorem that states that every set of real numbers can be decomposed into a perfect set and a set of Lebesgue measure zero

A theorem that states that every set of real numbers can be decomposed into a perfect set and a set of Baire measure zero

A theorem that states that every set of real numbers can be decomposed into a perfect set and a set of Hausdorff measure zero

A theorem that states that every set of real numbers can be decomposed into a perfect set and a set of Carathéodory measure zero

A theorem that states that every analytic set is Lebesgue measurable

A theorem that states that every analytic set is Baire measurable

A theorem that states that every analytic set is Hausdorff measurable

A theorem that states that every analytic set is Carathéodory measurable

A theorem that states that every analytic set is a Suslin set

A theorem that states that every analytic set is a Baire set

A theorem that states that every analytic set is a Polish set

A theorem that states that every analytic set is a Lebesgue measurable set

A theorem that states that every Suslin set is a Polish set

A theorem that states that every Suslin set is a Baire set

A theorem that states that every Suslin set is an analytic set

A theorem that states that every Suslin set is a Lebesgue measurable set

A theorem that states that every Lebesgue measurable set is a Suslin set

A theorem that states that every Lebesgue measurable set is a Baire set

A theorem that states that every Lebesgue measurable set is an analytic set

A theorem that states that every Lebesgue measurable set is a Polish set

An axiom that states that every family of sets of real numbers with the property that every two sets in the family have a non-empty intersection has a common element

An axiom that states that every family of sets of real numbers with the property that every two sets in the family have a non-empty intersection has a countable intersection

An axiom that states that every family of sets of real numbers with the property that every two sets in the family have a non-empty intersection has a perfect intersection

An axiom that states that every family of sets of real numbers with the property that every two sets in the family have a non-empty intersection has a Lebesgue measurable intersection

An axiom that states that every game of perfect information has a winning strategy

An axiom that states that every game of imperfect information has a winning strategy

An axiom that states that every game of chance has a winning strategy

An axiom that states that every game of skill has a winning strategy

A hypothesis that states that there is no set whose cardinality is greater than the cardinality of the set of natural numbers and less than the cardinality of the set of real numbers

A hypothesis that states that there is a set whose cardinality is greater than the cardinality of the set of natural numbers and less than the cardinality of the set of real numbers

A hypothesis that states that there is a set whose cardinality is equal to the cardinality of the set of natural numbers

A hypothesis that states that there is a set whose cardinality is equal to the cardinality of the set of real numbers

A hypothesis that states that for every set of real numbers, there is a set whose cardinality is greater than the cardinality of the set of natural numbers and less than the cardinality of the set of real numbers

A hypothesis that states that for every set of real numbers, there is a set whose cardinality is equal to the cardinality of the set of natural numbers

A hypothesis that states that for every set of real numbers, there is a set whose cardinality is equal to the cardinality of the set of real numbers

A hypothesis that states that for every set of real numbers, there is a set whose cardinality is greater than the cardinality of the set of natural numbers and greater than the cardinality of the set of real numbers