Timeline for Is the following theory countably axiomatizable?
Current License: CC BY-SA 3.0
14 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Dec 14, 2016 at 0:43 | comment | added | Joel David Hamkins | You are right. If he allowed set parameters, it would amount to GB+AC. | |
| Dec 14, 2016 at 0:04 | history | edited | David Pokorny | CC BY-SA 3.0 |
Language
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| Dec 13, 2016 at 23:48 | history | edited | David Pokorny | CC BY-SA 3.0 |
provide link to the new question
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| Dec 13, 2016 at 21:02 | comment | added | Noah Schweber | @JoelDavidHamkins I don't even think it's doing that - note that it only applies to parameter-free $\varphi$. | |
| Dec 13, 2016 at 19:45 | history | edited | David Pokorny | CC BY-SA 3.0 |
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| Dec 13, 2016 at 19:15 | comment | added | Joel David Hamkins | It seems to me that the theory basically amounts to GB+AC, since the naming process is simply ensuring instances of class comprehension. | |
| Dec 13, 2016 at 18:41 | answer | added | Noah Schweber | timeline score: 7 | |
| Dec 13, 2016 at 16:16 | review | Close votes | |||
| Dec 14, 2016 at 14:36 | |||||
| Dec 13, 2016 at 16:02 | comment | added | David Pokorny | Oh, sorry. I meant to say this: add a unary predicate $M x$ for "x is a set" and for each axiom in ZF, relativize it with respect to $M x$, so that the ZF axioms only apply to sets (except for the axiom of extension) and not the new constants. As in MK, $x$ is a set if and only if there exists $y$ such that $x\in y$. | |
| Dec 13, 2016 at 15:59 | comment | added | Emil Jeřábek | Anyway, it’s impossible to countably axiomatize a (consistent) theory in an uncountable language, unless all but countably many of the symbols are left completely arbitrary by the axioms. | |
| Dec 13, 2016 at 15:55 | comment | added | Emil Jeřábek | The way you defined it, $T_1$ (and a fortiori all subsequent theories) is inconsistent. You need to either start with a theory of classes rather than ZF, or use unary predicates instead of constants. | |
| Dec 13, 2016 at 15:28 | history | edited | David Pokorny | CC BY-SA 3.0 |
added 43 characters in body
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| Dec 13, 2016 at 15:19 | history | asked | David Pokorny | CC BY-SA 3.0 |