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	<a,b&62; is a set whose members occur in the order shown

			Full Idea: <a,b> is a set whose members occur in the order shown; <x1,x2,x3, ..xn> 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

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)

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)

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)

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)

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)

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)