Timeline for Is this first-order statement true? [closed]

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Mar 12, 2014 at 11:29	history	closed	Bjørn Kjos-Hanssen Andrey Rekalo Stefan Kohl♦ Ricardo Andrade Willie Wong		Not suitable for this site
Mar 12, 2014 at 7:14	review	Close votes
Mar 12, 2014 at 11:29
Jun 20, 2010 at 3:58	comment	added	rtg658		Thanks for that! I do apologise if that was an inappropriate question; I'm new to this site. Had I phrased it as a general inquiry into the naturals as a model/structure for NBG rather than a specific "is this true?" question, would it have been more appropriate?
Jun 20, 2010 at 3:53	comment	added	Joel David Hamkins		Your argument that $w=a$ works is correct. You may be interested in this MO answer mathoverflow.net/questions/12584/…, which is about the similar situation using the reals instead of the natural numbers.
Jun 20, 2010 at 3:49	comment	added	Joel David Hamkins		It is true. The union axiom asserts that for every set $x$, there is a set consisting precisely of the elements of elements of $x$. (Your version is weaker, since it is only one direction.) If you interpret sets as natural numbers and element of as $\lt$, then this translates in $\mathbb{N}$ to: for every natural number $n$, there is a number $m$ such that the numbers below $m$ are precisely the numbers that are below a number below $n$. This is true if we take $m=n-1$, using $m=0$ if $n=0$. Finally, this question may not be appropriate for MO, which is for research-level questions.
Jun 20, 2010 at 3:36	history	asked	rtg658	CC BY-SA 2.5