### 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
 9672 Free logic is one of the few first-order non-classical logics
 Full Idea: Free logic is an unusual example of a non-classical logic which is first-order. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], Pref)
###### 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
 9697 X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets
 Full Idea: X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets, the set of all the n-tuples with its first member in X1, its second in X2, and so on. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.0)
 9685
 Full Idea: is a set whose members occur in the order shown; is an 'n-tuple' ordered set. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10)
 9675 a ∈ X says a is an object in set X; a ∉ X says a is not in X
 Full Idea: a ∈ X means that a is a member of the set X, that is, a is one of the objects in X. a ∉ X indicates that a is not in X. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2)
 9674 {x; A(x)} is a set of objects satisfying the condition A(x)
 Full Idea: {x; A(x)} indicates a set of objects which satisfy the condition A(x). From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2)
 9673 {a1, a2, ...an} indicates that a set comprising just those objects
 Full Idea: {a1, a2, ...an} indicates that the set comprises of just those objects. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2)
 9677 Φ indicates the empty set, which has no members
 Full Idea: Φ indicates the empty set, which has no members From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4)
 9676 {a} is the 'singleton' set of a (not the object a itself)
 Full Idea: {a} is the 'singleton' set of a, not to be confused with the object a itself. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4)
 9679 X⊂Y means set X is a 'proper subset' of set Y
 Full Idea: X⊂Y means set X is a 'proper subset' of set Y (if and only if all of its members are members of Y, but some things in Y are not in X) From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6)
 9678 X⊆Y means set X is a 'subset' of set Y
 Full Idea: X⊆Y means set X is a 'subset' of set Y (if and only if all of its members are members of Y). From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6)
 9681 X = Y means the set X equals the set Y
 Full Idea: X = Y means the set X equals the set Y, which means they have the same members (i.e. X⊆Y and Y⊆X). From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6)
 9683 X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets
 Full Idea: X ∩ Y indicates the 'intersection' of sets X and Y, which is a set containing just those things that are in both X and Y. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8)
 9682 X∪Y indicates the 'union' of all the things in sets X and Y
 Full Idea: X ∪ Y indicates the 'union' of sets X and Y, which is a set containing just those things that are in X or Y (or both). From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8)
 9684 Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X
 Full Idea: Y - X indicates the 'relative complement' of X with respect to Y, that is, all the things in Y that are not in X. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8)
###### 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
 9688 A 'singleton' is a set with only one member
 Full Idea: A 'singleton' is a set with only one member. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4)
 9689 The 'empty set' or 'null set' has no members
 Full Idea: The 'empty set' or 'null set' is a set with no members. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4)
 9690 A set is a 'subset' of another set if all of its members are in that set
 Full Idea: A set is a 'subset' of another set if all of its members are in that set. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6)
 9691 A 'proper subset' is smaller than the containing set
 Full Idea: A set is a 'proper subset' of another set if some things in the large set are not in the smaller set From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6)
 9694 The 'relative complement' is things in the second set not in the first
 Full Idea: The 'relative complement' of one set with respect to another is the things in the second set that aren't in the first. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8)
 9693 The 'intersection' of two sets is a set of the things that are in both sets
 Full Idea: The 'intersection' of two sets is a set containing the things that are in both sets. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8)
 9692 The 'union' of two sets is a set containing all the things in either of the sets
 Full Idea: The 'union' of two sets is a set containing all the things in either of the sets From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8)
 9698 The 'induction clause' says complex formulas retain the properties of their basic formulas
 Full Idea: The 'induction clause' says that whenever one constructs more complex formulas out of formulas that have the property P, the resulting formulas will also have that property. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.2)
 9695 An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order
 Full Idea: An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10)
 9696 A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets
 Full Idea: A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10)
 9686 A 'set' is a collection of objects
 Full Idea: A 'set' is a collection of objects. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2)
 9687 A 'member' of a set is one of the objects in the set
 Full Idea: A 'member' of a set is one of the objects in the set. From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2)
###### 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
 9680 The empty set Φ is a subset of every set (including itself)
 Full Idea: The empty set Φ is a subset of every set (including itself). From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6)