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Math Help - Enderton 3.5 Problem 10

  1. #1
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    Enderton 3.5 Problem 10

    Here is problem 10 from Section 3.5 of Enderton's "A Mathematical Introduction to Logic":

    The theory Cn Ae has many complete extensions, of which ThN is but one. How many? That is, what is the cardinality of the set of complete theories (in the language) that extend Ae?

    Does anyone know how to answer this question?
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  2. #2
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    Re: Enderton 3.5 Problem 10

    I could search the book for the notations Cn, Ae and ThN, but to speed things up, could you remind what they stand for?
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  3. #3
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    Re: Enderton 3.5 Problem 10

    Ae is the set consisting of the following axioms:

    Enderton 3.5 Problem 10-new-bitmap-image.jpg

    CnAe is the set of all consequences of Ae.

    N = Enderton 3.5 Problem 10-new-bitmap-image.jpg is a model of Ae. ThN is the set of all sentences true in N.
    Last edited by Exler; April 21st 2013 at 01:21 PM.
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