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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 III p.123 Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics
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 says if the sentences are countable, so is the model
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.282 Tarski and Vaught established the equivalence relations between first-order structures