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Suppose I'm working in a language of equality in which the only non-logical symbol is the 2-place relation symbol =. I'm trying to find all possible atomic formulas that can be represented in this language.

Would they be:

  1. x=x
  2. x=y
  3. t1=t1
  4. t1=t2

where x and y are variables in the language and t1 and t2 are terms in the language?

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If there are no function symbols, there aren't very many terms possible. – Chris Eagle Dec 19 '11 at 19:53
up vote 0 down vote accepted

You are correct, although a little redundant.

You have to keep in mind that saying "$x=y$ is an atomic formula for all variable symbols $x, y$" does not preclude the possibility that $x$ and $y$ are actually the same variable symbol. Similarly for terms. (This is similar to "regular" mathematics where saying "$x+y$ is a real number for all real numbers $x,y$" does not mean that $x$ and $y$ necessarily denote different real numbers.)

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