Timeline for Possible no standard use of replacement axiom
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 24, 2016 at 20:51 | vote | accept | Carlos Freites | ||
| May 25, 2014 at 19:21 | comment | added | Carlos Freites | By taking the Real numbers as a Complete Field constant, I have made optional construct it. Thank you. | |
| May 25, 2014 at 1:43 | comment | added | Andreas Blass | By including $\phi$, we get a construction that directly incorporates both replacement (by taking $\phi(x)$ to be some formula that is true for all $x$, like for example $x=x$) and separation (by taking $t(x)$ to be simply $x$), without going through the (easy but somewhat unnatural) process of getting separation as a special case of replacement. Whether one can get by without $\phi$ altogether depends on how rich a supply of terms one has; you indicated that you add some terms by extending the language of ZFC, but it may matter how widely you extend the language. | |
| May 24, 2014 at 21:08 | comment | added | Carlos Freites | Thank you. Your assumption is right "For all SET(z)" means "For all set". About the lack of function symbol in ZFC, is just because that, I used the theorem in a language I built based in ZFC. On the other hand, in the notation you cited {t(x):x∈A:ϕ(x)} I can not see where the formula ϕ(x) come from, would not be enough {t(x):x∈A} because what is given are the set A and the term t(x). Thanks again, your answer is a relief to me. | |
| May 24, 2014 at 20:21 | history | answered | Andreas Blass | CC BY-SA 3.0 |