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Genericphenomenaingroups–Someanswersandmany Questions
4 
 IGORRIVIN 
 f 
 irst, let’s talk about what it means for some property P to be generic for some 
 (possibly) infinite (but countable) set S. 
 3. Anidealist approach to randomness 
 First, define a measure of size v on the elements of S. This should satisfy some 
 simple axioms, such as: 
 (1) v(x) ≥ 0 for all x ∈ S. 
 (2) The set Sk = {x ∈ S|v(x) ≤ k} is finite for every k. 
 Let now P be a predicate on the elements of S– think of a predicate as just a 
 function from S to {0,1}...