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]].

green numbers give full details    |     back to texts     |     expand these ideas

---

4. Formal Logic / E. Nonclassical Logics / 6. Free Logic

9672	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

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

9695	An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order

9696	A 'cartesian product' of sets is the set of all the n-tuples 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

9698	The 'induction clause' says complex formulas retain the properties of their basic formulas

9688	A 'singleton' is a set with only one member

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

9692	The 'union' of two sets is a set containing all the things in either of the sets

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

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)