This page is your portal to the heart of the book: the details of the known consequence implications
of the various forms of the axioms of choice vis-a-vis each other. The book classifies the results as follows:
| Code |
Description |
| 1: \( A \Rightarrow B\) |
A result is given a classification of '1' if there is a published result proving the implication. |
| 2: \(A \Rightarrow B\) |
A result is given a classification of '2' if there is a chain of code 1 implications beginning with
form \(A\) ending with form \(B\).
|
| 3: \(A \not \Rightarrow B\) |
A result is given a classification of '3' if there is a published proof that there is a specific
\(ZF\) set theory model \(\frak M\) in which both form \(A\) is true and form \(B\) is false.
|
| 4: \(A \not \Rightarrow B\) |
A result is given a classification of '4' if there is shown to be a chain of implications which
imply the existence of a \(ZF\) set theory model \(\frak M\) in which both form \(A\) is true and
form \(B\) is false |
| 5: \(A \not \Rightarrow B\) |
A result is given a classification of '5' if there is a published proof that there is a specific
\(ZF^{0}\) set theory model \(\frak N\) in which both form \(A\) is true and form \(B\) is false.
|
| 6: \(A \not \Rightarrow B\) |
A result is given a classification of '6' if there is shown to be a chain of implications which
imply the existence of a \(ZF^{0}\) set theory model \(\frak N\) in which both form \(A\)
and form \(B\) is false.
|