Ideas from 'Intro to NonClassical Logic (1st ed)' by Graham Priest [2001], by Theme Structure
[found in 'Introduction to NonClassical Logic' by Priest,Graham [CUP 2001,052179434x]].
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4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
9672

Free logic is one of the few firstorder nonclassical logics

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

9685

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

9675

a ∈ X says a is an object in set X; a ∉ X says a is not in X

9674

{x; A(x)} is a set of objects satisfying the condition A(x)

9673

{a1, a2, ...an} indicates that a set comprising just those objects

9677

Φ indicates the empty set, which has no members

9676

{a} is the 'singleton' set of a (not the object a itself)

9679

X⊂Y means set X is a 'proper subset' of set Y

9678

X⊆Y means set X is a 'subset' of set Y

9681

X = Y means the set X equals the set Y

9683

X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets

9682

X∪Y indicates the 'union' of all the things in sets X and Y

9684

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
9694

The 'relative complement' is things in the second set not in the first

9693

The 'intersection' of two sets is a set of the things that are in both sets

9692

The 'union' of two sets is a set containing all the things in either of the sets

9698

The 'induction clause' says complex formulas retain the properties of their basic formulas

9688

A 'singleton' is a set with only one member

9687

A 'member' of a set is one of the objects in the set

9695

An 'ordered pair' (or ordered ntuple) is a set with its members in a particular order

9696

A 'cartesian product' of sets is the set of all the ntuples with one member in each of the sets

9686

A 'set' is a collection of objects

9689

The 'empty set' or 'null set' has no members

9690

A set is a 'subset' of another set if all of its members are in that set

9691

A 'proper subset' is smaller than the containing set

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)
