Open thread, Oct. 12 - Oct. 18, 2015

MrMind

If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

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If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

Notes for future OT posters:

1. Please add the 'open_thread' tag.

2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)

3. Open Threads should be posted in Discussion, and not Main.

4. Open Threads should start on Monday, and end on Sunday.

If there's any sort of inconsistency in ZF or PA or any other major system currently in use, it will be much harder to find than this.

Indeed, since you can prove ZFC consistent with the aid of an inaccessible cardinal. And you can prove the consistency of an inaccessible cardinal with a Mahlo cardinal, and so on.

I'm not sure that's strong evidence for the thesis in question. If ZFC had a low-lying inconsistency, ZFC+an inaccessible cardinal would still prove ZFC consistent, but it would be itself an inconsistent system that was effectively lying to you. Same remarks apply to any large cardinal axiom.