When one already has a PhD from a university outside of Europe, could he apply for a second PhD in Austria?
I know that second PhD is not possible for example in UK. Is it the same for Austria? Is there anything against it?
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Assuming that "apply for a PhD" means that you want to persue a second PhD in Austria; yes that's fine. You can get as many PhDs as you want, but you cannot use the same research for more than one PhD and you cannot do the same program (same university, field and title) twice as far as I know.
If you are asking if you can use your research which was used for getting the PhD in a different country to get one in Austria the no, that's not allowed.
It is allowed to do second Phd. in the UK. Nothing prevent that. But the point of Phd. is training to do research. Once you pass this, you can do research and the scientific community knows that you have passed the training required to do research.
Multiple Phd. is not an honour or will look better in a CV. Both in Phd. and Post doctoral position you will do research. You will be evaluated on your research outcome. Not on how many degrees you have. If you have 3 Phds. and no publications and another person have one Phd. and three good publications, I think mostly, the student with one Phd. will look better on the employers' eyes. Because he showed outcome.
But it is totally up to you. If you are not satisfied with your first Phd. and could not get a job, then if you could get another Phd. can be a choice and chance to do better.
But if you just wan to continue research and reading, all post doc. positions do similar work as the Phd. They do research but may be with more responsibilities.