Ideas from 'Intro to Non-Classical Logic (1st ed)' by Graham Priest [2001], by Theme Structure

[found in 'Introduction to Non-Classical Logic' by Priest,Graham [CUP 2001,0-521-79434-x]].

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4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
Free logic is one of the few first-order non-classical logics
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
{a1, a2,} indicates that a set comprising just those objects
X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets
<a,b&62; is a set whose members occur in the order shown
a ∈ X says a is an object in set X; a ∉ X says a is not in X
{x; A(x)} is a set of objects satisfying the condition A(x)
Φ indicates the empty set, which has no members
{a} is the 'singleton' set of a (not the object a itself)
X⊆Y means set X is a 'subset' of set Y
X⊂Y means set X is a 'proper subset' of set Y
X = Y means the set X equals the set Y
X∪Y indicates the 'union' of all the things in sets X and Y
X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets
Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
The 'empty set' or 'null set' has no members
A 'proper subset' is smaller than the containing set
A set is a 'subset' of another set if all of its members are in that set
The 'union' of two sets is a set containing all the things in either of the sets
The 'intersection' of two sets is a set of the things that are in both sets
The 'relative complement' is things in the second set not in the first
The 'induction clause' says complex formulas retain the properties of their basic formulas
A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets
An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order
A 'member' of a set is one of the objects in the set
A 'set' is a collection of objects
A 'singleton' is a set with only one member
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
The empty set Φ is a subset of every set (including itself)