20 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] |
15567 | Some events involve no change; they must, because causal histories involve unchanges [Lewis] |
15561 | The events that suit semantics may not be the events that suit causation [Lewis] |
15565 | Events have inbuilt essences, as necessary conditions for their occurrence [Lewis] |
15566 | Events are classes, and so there is a mereology of their parts [Lewis] |
15564 | An event is a property of a unique space-time region [Lewis] |
15563 | Properties are very abundant (unlike universals), and are used for semantics and higher-order variables [Lewis] |
15562 | Causation is a general relation derived from instances of causal dependence [Lewis] |
1558 | Clearly the gods ignore human affairs, or they would have given us justice [Thrasymachus] |