Timeline for Given is "model". How many theories may it be a model?
Current License: CC BY-SA 2.5
6 events
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| Feb 8, 2010 at 15:26 | comment | added | Joel David Hamkins | The theories T_A are different, in the sense that there are models distinguishing any two of them, but they are all completely trivial. They just say that the structure has a size that is not in A. The theories T' in my last paragraph, however, are not trivial. These theories assert what the model could have been like, if sigma had been true. Since sigma is not true, these theories are vacuously true in M, but the theories are really talking about what might have been true in another structure. I take this to show that we should investigate all models, rather than theories true in one model. | |
| Feb 8, 2010 at 15:09 | comment | added | kakaz | "This shows that in fact every model M, in any language, satisfies at least continuum many deductively closed theories. " So we are completely lost in the space of models. Are there some minimal closed theories which are true in given model? Or all of them are completely different? | |
| Feb 8, 2010 at 14:36 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
Fixed issue with empty language
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| Feb 8, 2010 at 14:24 | vote | accept | kakaz | ||
| Feb 8, 2010 at 13:52 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
deleted 196 characters in body; deleted 23 characters in body
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| Feb 8, 2010 at 13:47 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |