Combining Texts
Ideas for
'Parmenides', 'Substances without Substrata' and 'Foundations without Foundationalism'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
7 ideas
4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set
13651
|
A set is 'transitive' if contains every member of each of its members [Shapiro]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13647
|
Choice is essential for proving downward Löwenheim-Skolem [Shapiro]
|
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
13631
|
Are sets part of logic, or part of mathematics? [Shapiro]
|
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
13654
|
It is central to the iterative conception that membership is well-founded, with no infinite descending chains [Shapiro]
|
13640
|
Russell's paradox shows that there are classes which are not iterative sets [Shapiro]
|
13666
|
Iterative sets are not Boolean; the complement of an iterative set is not an iterative sets [Shapiro]
|
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
13653
|
'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element [Shapiro]
|