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
9673

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

9674

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

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

9681

X = Y means the set X equals the set Y

9678

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

9682

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

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

9683

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

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
9695

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

9690

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

9688

A 'singleton' is a set with only one member

9691

A 'proper subset' is smaller than the containing set

9694

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

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

9687

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

9689

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

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

9693

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

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)
