Hi, I have stumbled upon PF many times through Google, but this is my first time posting. Hopefully, someone will be able to help me out.(adsbygoogle = window.adsbygoogle || []).push({});

My question is about the concept of elementary equivalence in logic. According to my book, two structures A and B are elementary equivalent if: for every sentence s: A satisfies s if and only if B satisfies s. However, in my book it is also said that if B satisfies the theory of A, then A and B are elementary equivalent.

It is obvious that if this A satisfies s, then B also satisfies s (since s is in the theory of A). But I don't see how to get the other side of the "if and only if". If B satisfies s, I see no reason for s to be also satisfied by A. If B satisfies the theory of A, B could just as well satisfy other sentences too, right?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Satisfiability vs Elementary equivalence

Loading...

Similar Threads - Satisfiability Elementary equivalence | Date |
---|---|

Elementary set theory | Dec 17, 2014 |

Need a real life example that satisfies the property? | May 10, 2013 |

Mathematical Logic, Interpretation, Satisfiable, Consequence relation | Jan 29, 2012 |

Alexsandro, am I gonna win a prize, or will have to be satisfied with being helpful? | Aug 28, 2005 |

Reading about the property of satisfiability | Jul 20, 2005 |

**Physics Forums - The Fusion of Science and Community**