2004 | Alfred Tarski: life and logic |
Ch.9 | p.228 | 10156 | 'Recursion theory' concerns what can be solved by computing machines |
Int I | p.43 | 10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy |
Int I | p.44 | 10147 | The Axiom of Choice is consistent with the other axioms of set theory |
Int I | p.46 | 10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets |
Int I | p.47 | 10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition |
Int I | p.48 | 10150 | The Trichotomy Principle is equivalent to the Axiom of Choice |
Int III | p.123 | 10154 | Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics |
Int IV | p.193 | 10155 | Both Principia Mathematica and Peano Arithmetic are undecidable |
Int V | p.280 | 10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? |
Int V | p.281 | 10160 | Löwenheim-Skolem says if the sentences are countable, so is the model |
Int V | p.281 | 10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory |
Int V | p.281 | 10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory |
Int V | p.282 | 10162 | Tarski and Vaught established the equivalence relations between first-order structures |