21 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] |
17813 | Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP] |
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] |
17812 | Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP] |
20937 | The state should produce higher civilisations for all, in tune with the economic apparatus [Gramsci] |
20935 | Eventually political parties lose touch with the class they represent, which is dangerous [Gramsci] |
20936 | Caesarism emerges when two forces in society are paralysed in conflict [Gramsci] |
20941 | Totalitarian parties cut their members off from other cultural organisations [Gramsci] |
20939 | What is the function of a parliament? Does it even constitute a part of the State structure? [Gramsci] |
20938 | Liberalism's weakness is its powerful rigid bureaucracy [Gramsci] |
20940 | Perfect political equality requires economic equality [Gramsci] |