Tessellate S.T.E.M.S. (2019) - Computer Science - College - Set 2 - Objective Problem 5

Computer Science Level pending

Suppose Σ \Sigma is a first order language. Say A \mathfrak{A} and B \mathfrak{B} are Σ \Sigma -models.

Consider the two following statements:

  1. A \mathfrak{A} and B \mathfrak{B} are isomorphic.
  2. A ϕ \mathfrak{A} \models \phi if and only if B ϕ \mathfrak{B} \models \phi for any first order sentence ϕ \phi

Which of the following is true?


This problem is a part of Tessellate S.T.E.M.S (2019)

Both of them 1 2 1 \implies 2 None of them 2 1 2 \implies 1

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