14446 | We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell] |
14443 | The British parliament has one representative selected from each constituency [Russell] |
14444 | Choice is equivalent to the proposition that every class is well-ordered [Russell] |
14445 | Choice shows that if any two cardinals are not equal, one must be the greater [Russell] |
10196 | The Axiom of Choice needs a criterion of choice [Black] |
10542 | To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett] |
13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
12321 | The axiom of choice must accept an indeterminate, indefinable, unconstructible set [Badiou] |
18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
13036 | Choice: ∀A ∃R (R well-orders A) [Kunen] |
18270 | Choice suggests that intensions are not needed to ensure classes [Coffa] |
13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
13647 | Choice is essential for proving downward Löwenheim-Skolem [Shapiro] |
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
10208 | Axiom of Choice: some function has a value for every set in a given set [Shapiro] |
10252 | The Axiom of Choice seems to license an infinite amount of choosing [Shapiro] |
15717 | Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan] |
10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
10676 | The Axiom of Choice is a non-logical principle of set-theory [Hossack] |
10686 | The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack] |