Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Second-order variables: elements of domain only without quantifiers?

  1. Jan 4, 2013 #1
    On one side one can define second-order variables as ranging over all elements of Pk(M) for all natural numbers k (P=power set of M, M is the universe of the model, superscript being iteration). On the other side it is sometimes defined as ranging over all first-order relations and predicates. In this latter definition, does "predicates" include first-order sentences with quantifiers and variables, or only first-order sentences with only constant symbols?
    Thanks.
     
  2. jcsd
  3. Jan 4, 2013 #2
    er, sorry, I meant P(Mk), where the exponent refers to the Cartesian product
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Second-order variables: elements of domain only without quantifiers?
  1. Second-order logic (Replies: 8)

Loading...