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I'm wondering how to go about publishing or even submitting a paper.

I'm fairly sure that apart from the research on the paper, one must be sure that no one has published an article or thesis on that exact subject. This much, I think I've accomplished.

I'm not sure that what I did was all 100% correct and I know I should know that. It seems okay to me but I was hoping that the editor would work with me since this is my first time and not reject me permanently for having a flawed work; maybe even tell me what to fix before I can submit it. Maybe I might as well keep dreaming on that regard.

I think the second step would be to find a journal with similar interests. I believe the Journal of Symbolic Logic would be the right journal for me, though there are definitely more than one out there where my paper would belong.

And what about arxiv.org? What's up with that?

I'm specifically looking for feedback from those who have successfully written and published papers before; I dunno, maybe mathwonk, matt grime, or hurkyl (in no order). Any feedback is definitely appreciated.

Thank you.