i would like to know how to show form the above sentence that every model of phi_n must have at least n elements in the underlying set

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- Mar 20th 2011, 04:41 PMMike12model

i would like to know how to show form the above sentence that every model of phi_n must have at least n elements in the underlying set - Mar 21st 2011, 01:36 AMemakarov
If is , then is not a sentence since is a free variable.

A remark concerning notation. Subscripts consisting of more than one symbol must be enclosed in parentheses or braces. Otherwise, it is not clear whether X_n-1 means or . You can use /\, \/ and ~ to denote conjunction, disjunction and negation, respectively, in ASCII. It is also not too hard to write LaTeX code for these formulas. The formula above is produced by [tex]\forall x_1,\dots,x_{n-1}.x_n\ne x_1\land\dots\land x_n\ne x_{n-1}[/tex]. Also, \lor produces , \neg produces and \exists gives .