Timeline for Looking for a source for Intended Interpretation
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 6, 2016 at 18:50 | history | edited | Gabriel Nivasch | CC BY-SA 3.0 |
added 83 characters in body
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| Mar 6, 2016 at 18:49 | comment | added | Gabriel Nivasch | Well, that's on page xix (section "Notation"). He says that $\mathbb N$ is the set of natural numbers -- "including zero", just in case! | |
| Mar 6, 2016 at 15:19 | comment | added | Mikhail Katz | the source you mentioned does not say that N is the "intended interpretation". I was hoping to find some references containing the idea that the ordinary/usual/counting,etc integers are the intended interpretation of N. | |
| Mar 6, 2016 at 8:41 | history | edited | Gabriel Nivasch | CC BY-SA 3.0 |
Added ref to page 42 (definition of + and *)
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| Mar 6, 2016 at 8:36 | comment | added | Mikhail Katz | Great, I did not notice that at first. Gabriel, would you care to incorporate this additional information into your answer? | |
| Mar 3, 2016 at 18:37 | comment | added | Gabriel Nivasch | Do you mean that Wang writes "... $+$ and $\cdot$ as standing for ordinary addition and multiplication"? Rautenberg also says that: At the beginning of section 2.1 "Mathematical structures" (page 42 in the 3rd edition) he writes "$\mathcal A = (\mathbb N, <, +, \cdot, 0, 1)$ is an example with the domain $\mathbb N$; here $<$, $+$, $\cdot$, $0$, $1$ again have their ordinary meaning." So later on, on section 3.3 when he says $+$ and $\cdot$, he presumably means that already-defined ordinary meaning. | |
| Mar 3, 2016 at 15:34 | comment | added | Mikhail Katz | ...I suppose it is in the nature of an encyclopedia article that Wang would try to explain this, but still I am interested in having a properly published source. | |
| Mar 3, 2016 at 15:34 | comment | added | Mikhail Katz | The discussion of $\mathbb{N}$ is on page 83 in the second edition of Rautenberg (section 3.3). However, he does not say anything about the standard model, limiting himself to denoting it. Note that Wang in the comment cited in my question tried to establish a correspondence between the standard model and the ordinary numbers and ordinary addition and multiplication, but Rautenberg doesn't discuss this aspect of the Intended Interpretation, presumably assuming that it is understood... | |
| Mar 3, 2016 at 13:03 | history | answered | Gabriel Nivasch | CC BY-SA 3.0 |