19 ideas
| 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] |
| 10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
| 10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
| 10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
| 10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
| 10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
| 10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
| 10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
| 10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
| 8329 | Either causal relations are given in experience, or they are unobserved and theoretical [Sosa/Tooley] |
| 8324 | The problem is to explain how causal laws and relations connect, and how they link to the world [Sosa/Tooley] |
| 8328 | Causation isn't energy transfer, because an electron is caused by previous temporal parts [Sosa/Tooley] |
| 8327 | If direction of causation is just direction of energy transfer, that seems to involve causation [Sosa/Tooley] |
| 8330 | Are causes sufficient for the event, or necessary, or both? [Sosa/Tooley] |
| 8325 | The dominant view is that causal laws are prior; a minority say causes can be explained singly [Sosa/Tooley] |
| 9425 | Lewis later proposed the axioms at the intersection of the best theories (which may be few) [Mumford on Lewis] |