[DOC] [TLE] Set theory - Wikipedia [PAR] Set theory is a branch of mathematical logic that studies sets, which informally 
are collections of ... A derived binary relation between two sets is the subset 
relation, also called set inclusion. If all the members of set A are also members of 
set B, then A is a subset of B, denoted A  B. For example, .... Sets and proper 
classes. [DOC] [TLE] Class (set theory) - Wikipedia [PAR] In set theory and its applications throughout mathematics, a class is a collection 
of sets that can ... Please help improve it or discuss these issues on the talk page. 
... A class that is not a set (informally in ZermeloFraenkel) is called a proper 
class, .... set theory admits proper classes as basic objects, like NBG, but also 
allows... [DOC] [TLE] Set (mathematics) - Wikipedia [PAR] In mathematics, a set is a well-defined collection of distinct objects, considered as 
an object in ... Developed at the end of the 19th century, set theory is now a 
ubiquitous part of ... The objects that make up a set (also known as the elements 
or members of a set) ... We can illustrate these two important points with an 
example:. [DOC] [TLE] Mathematical logic - Wikipedia [PAR] For Quine's theory sometimes called "Mathematical Logic", see New Foundations
. "Mathematical formalism" redirects here. For the philosophical view, see 
Formalism (philosophy of mathematics). Mathematical logic is a subfield of 
mathematics exploring the applications of formal logic to ... These areas share 
basic results on logic, particularly first-order logic, and... [DOC] [TLE] Boolean algebra - Wikipedia [PAR] In mathematics and mathematical logic, Boolean algebra is the branch of algebra 
in which the .... Boolean algebra also deals with functions which have their 
values in the set {0, 1}. ... As with elementary algebra, the purely equational part 
of the theory may be .... The first operation, x  y, or Cxy, is called material 
implication. [DOC] [TLE] Theory (mathematical logic) - Wikipedia [PAR] In mathematical logic, a theory is a set of sentences in a formal language. Usually 
a deductive system is understood from context. An element   T {\displaystyle \
phi \in T} \phi \in T of a theory T {\displaystyle T} T is then called an axiom of the 
theory, and any sentence that follows from the ... These initial statements are 
often called the primitive elements or elementary... [DOC] [TLE] Russell's Paradox (Stanford Encyclopedia of Philosophy) [PAR] Dec 8, 1995 ... Also known as the Russell-Zermelo paradox, the paradox arises ... in logic, set 
theory and the philosophy and foundations of mathematics. ... If it is, it is one of 
those classes that are not members of themselves, i.e., it is not a member of itself. 
.... in large part by adoption of the so-called vicious circle principle. [DOC] [TLE] Set Theory (Stanford Encyclopedia of Philosophy) [PAR] Oct 8, 2014 ... Set theory is the mathematical theory of well-determined collections, called sets, 
of objects that are called members, or elements, of the set. .... (MK), allow also for 
a formal treatment of proper classes. 2. The axioms of set theory. ZFC is an axiom 
system formulated in first-order logic with equality and with... [DOC] [TLE] Mathematical Logic as Based on the Theory of Types - JStor [PAR] mendation; it has also, if I am not mistaken, a certain consonance with common ... 
be solved, and shall then show how the theory of logical types effects their ... (2) 
Let w be the class of all those classes which are not members of them- ... Dixon, " 
On ' well-ordered ' aggregates," Proc. London Xath. Soc., Series 2, Vol. IV, Part I. [DOC] [TLE] Introduction to Mathematical Philosophy [PAR] The beginnings of mathematical logic are less definitely known than its later ... 
appears to invalidate much traditional philosophy, and even a good deal

Question: The "theory" of membership in these, also called classes, is part of mathematics as well as logic
Answer: Sets