I wrote some texts related to mathematical logic: http://www.mathematics21.org/formulas.html

How to check if my ideas are novel? Where and who to ask?

The problem is that I am not even nearly a professional logician.

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    This question is probably more suitable for math.stackexchange Apr 18 '18 at 17:45
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    @user_of_math: The question is how. Your comment is an answer.
    – Wrzlprmft
    Apr 18 '18 at 17:46
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    The reality is unless you’re in academia and have an advisor, or are close to relevant people in the field who you can to for for advice or ask favors of, no one has any motivation to investigate some unknown person’s work in a field he doesn’t “live” in. Think about it from the reviewer’s perspective: what does he get out of doing the work? That said, I suppose one approach would to try to find a relevant journal that’s not too competitive and submit your work there. But I wouldn’t hold my breath.
    – Dan Bron
    Apr 18 '18 at 18:47
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    Side note about the content: You seem to have a different definition of "basis" than every other mathematician alive. Your document demonstrates that you know a lot of math words, but you should not repurpose them in a new context without a lot of explanation of why that makes sense. Apr 18 '18 at 20:21
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    you should not repurpose them in a new context without a lot of explanation of why that makes sense --- Also, there are no references directing the reader to similar work and to background material, which is especially needed since the exposition is not very complete. For example, in the statement "A basis[1] is a pair of a set E and some set X (set of indices or indexes) of functions on E", the reader is left in the dark concerning the co-domain of those functions defined on E. Also, "function from E_1 to E_2 an operator from" --- is there a reason to use "operator" instead of "function"? Apr 19 '18 at 0:36

The best way of finding out if your ideas are novel is to do a literature search.

A good place to start would be arxiv.org, which is a well-known pre-print repository (i.e. place where papers get uploaded before they are published) that has plenty of mathematical papers.

See what research has been done in the same area as you and you will get an idea of whether or not your research is novel, as well as the standard your work needs to reach if you intend to publish it in the future.

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    +1: People often post on Math SE asking if something is novel, protesting that they don't understand the literature well enough to tell if their work is novel. That's a dead giveaway that the work isn't. Apr 18 '18 at 20:23

There is no way except to put in the study necessary to have the knowledge of a professional logician. (This can easily take several years.)

Here is the fundamental problem. It is very possible that your ideas would look novel to a layperson, even a layperson who has read the relevant literature, but any professional logician would know that your ideas are really some old (possibly a century old) idea recast into new language by a standard well known trick that has already been used many times in the past.

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