tag:blogger.com,1999:blog-4987609114415205593.post5789933838484198098..comments2024-03-28T13:40:26.497+00:00Comments on M-Phi: Axiomatizations of arithmetic and the first-order/second-order divideJeffrey Ketlandhttp://www.blogger.com/profile/01753975411670884721noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-4987609114415205593.post-60516697931227932692016-01-16T21:13:50.738+00:002016-01-16T21:13:50.738+00:00I am also work on short paper this article give us...I am also work on short paper this article give us good idea how solve my math asthmatic question on short paper thanks for sharing <a href="http://www.paraphrasingservices.net/" rel="nofollow">paraphrasing service</a> .Allen jeleyhttps://www.blogger.com/profile/10312119051975318074noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-35876365783298644252014-02-12T07:37:28.893+00:002014-02-12T07:37:28.893+00:00Thanks, these are useful comments!Thanks, these are useful comments!Catarinahttps://www.blogger.com/profile/03277956118114314573noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-37360720363100333192014-02-11T18:36:07.655+00:002014-02-11T18:36:07.655+00:00Two remarks:
1) PA2 is "descriptively comple...Two remarks: <br />1) PA2 is "descriptively complete" only because and when you assume it is, that is, you assume that "the set of all subsets" is well-defined, well-understood and determinate (in the platonistic heaven). Of course, in practice, you can know about it only as much as your background (first-order) set theory (or whatever) allows you to prove about it. So, in reality, you only get out what you put in, so to say. <br />2) It is at least misleading to say that PA1 is "deductively stronger". You can look at PA2 as a normal theory in the two-sorted first-order logic, and as such, it is deductively stronger than PA1: it proves, e.g, the consistency of PA1.Panu Raatikainenhttp://www.mv.helsinki.fi/home/praatika/noreply@blogger.com