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Collection of Well-Formed Formulas with no Equivalent, Independent Subset

  1. Dec 2, 2011 #1

    jgens

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    Gold Member

    1. The problem statement, all variables and given/known data

    Find a collection of well-formed formulas Ʃ such that Ʃ has no independent equivalent subset.

    2. Relevant equations

    N/A

    3. The attempt at a solution

    So far I have been able to show that Ʃ must be infinite. However, after this, I get stuck. Could anyone give me a hint on how to construct such a Ʃ?

    Thanks!
     
  2. jcsd
  3. Dec 2, 2011 #2

    jgens

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    Gold Member

    I figured it out. If we take [itex]\Sigma = \{A_1, A_1 \wedge A_2, \dots, A_1 \wedge \cdots \wedge A_n, \dots\}[/itex], then that should work.
     
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