Isomorphisms of models. (in logic).

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The discussion focuses on identifying isomorphic models in logic, specifically five models defined with unary symbols and operations. The models include integers and rationals with various operations, and the conclusion is that models A and B are isomorphic, as well as models C and D. The participant expresses confusion about the initial question and requests clarification or resources for better understanding. A link to a relevant resource on isomorphism of models is provided for further exploration. This thread highlights the complexity of model theory in logic and the importance of understanding isomorphisms.
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suppose our language contains one unary syombol function.
we are given the next 5 models:
A=<Z,x+1> B=<Z,x-1> C=<Q,-x> D=<Z,-x> E=<Q,x^2>
write which of the models are isomorphic to each other.
where Z is the integer set, and Q is the ratioanls set.

my answer is that: A isomorphic to B, and C isomorphic to D, and these are the only isomorphisms.
 
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I don't understand your question, but I am curious.
Could you explain it, or could you give me a link where I could find the basic definitions to understand you questions.

Thanks,

Michel
 
The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...

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