Timeline for Can the proper/whole domain relationship in bi-interpretations be reversed for non-synonymous theories?
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| Feb 16 at 6:15 | comment | added | Zuhair Al-Johar | @JoelDavidHamkins, using tuples and congruences reminds me of the way you proved bi-interpretability between set theoretic mereology with bottom and that without it. Anyhow, the interpretations I'm speaking about doesn't necessarily do it that way. So, yes, the interpretations may not use $k$-tuples nor quotients by congruence. | |
| Feb 16 at 0:06 | comment | added | Joel David Hamkins | In the general case, according to the usage I usually follow, bi-interpretations allow one to represent the interpretated individuals using $k$-tuples in the interpreting realm (like interpreting $\mathbb{C}$ in $\mathbb{R}$), and also allowing the quotient by a definable equivalence relation, a congruence with respect to the interpreted structure, (like interpreting $\mathbb{Q}$ in $\mathbb{Z}$). But the way you refer to the interpreted domain being a subclass suggest that you are thinking that the interpretation does not use $k$-tuples and also no quotient by a congruence. Is that correct? | |
| Feb 15 at 21:33 | history | asked | Zuhair Al-Johar | CC BY-SA 4.0 |