green numbers give full details.     |    back to list of philosophers     |     expand these ideas

Ideas of Feferman / Feferman, by Text

[American, fl. 2004, He a professor at Stanford, she an independent scholar]

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