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

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 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

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)