Comments (7)
The classical theorems are there for a reason, to show that we can derive all the original stuff with ax-3
, and also to mark theorems that are either known to require classical reasoning, or haven't yet been "intuitionized". I don't think any marking is necessary, we already have ax-3
tracking in the HTML, although mentioning it in the text when the usage is deliberate is fine. If we insist on an explicit annotation then of course (New usage is discouraged.) should do the trick.
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Moving ax-3 later in the file is also something which occurred to me.
I'm trying to make the whole file clearer about things like the difference between "known to require classical reasoning" and "haven't yet been intuitionized". But I am open to a variety of ways to get there.
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My current thinking is roughly this:
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Remove stuff which is easy to remove and doesn't accomplish anything in iset.mm. I'm thinking of things like Nicod's axioms (which are an alternative axiomization of classical propositional logic, not intuitionistic propositional logic).
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Start chipping away at predicate logic by trying to decide whether things like ax12o (and others which depend on ax-3) can just be removed (and their usages replaced with other theorems), or proved intuitionistically, or what. Much of the ax-*o stuff makes sense in terms of a classical history and trying to carry it over to intuitionistic logic doesn't make much sense to me, but the details here will depend on seeing where it is used.
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At some point in this process (after step 1 and maybe after some of step 2), move ax-3 (and everything which still depends on it) to the end of the file.
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I like the idea of trying to use similar names in set.mm and iset.mm but even with that script it might be a bit labor intensive. Maybe I'll get the chance to take a closer look at a bulk rename at some time in the future, or maybe I'll just apply changes by hand when I notice them.
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Submitted as #169
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I guess maybe I have a weak preference for full names rather than initials but if people are looking at the contributor list I can take a look at some point.
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It will be a while before the work outlined above is done, but it is well underway, as people can see from all the recent changes to iset.mm. I'm going to close this issue as I think the path here is now pretty clear. Thanks to everyone for the comments and suggestions.
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Related Issues (20)
- Prove that Markov's Principle implies Post's theorem (iset.mm)
- CCHOICE and countably infinite versus countable HOT 7
- Typo in the description for Theorem rexbidvaALT HOT 1
- should iset.mm have both ax-bndl and ax-i12 ? HOT 2
- Appropriate names for +g and gsum HOT 1
- Appropriate name (and new symbol) for LSSum HOT 4
- Barycentric coordinates HOT 2
- Existence of a certain non-constant function implies the limited principle of omnisience HOT 4
- If not equal implies apart, Markov's principle follows HOT 1
- Updating mmset.html HOT 12
- Symbol and token for the class of semigroups HOT 9
- Update of the topological structure overview figure HOT 4
- Can a space filling curve exist in iset.mm? HOT 5
- The sine function is decreasing over [2,4] HOT 17
- Making SymGrp a structure restriction of EndoFMnd HOT 7
- Discourage indirect usage of ax-13? HOT 17
- Hypotheses with an "is a set" property using the universal class _V HOT 4
- Newbie here, I created a proof with mmj2. How do I add the proof to the database HOT 17
- </table> tags in AS's mathbox are outside <html> blocks HOT 3
- Interchanging factors in integrals and sums (Lemmas for AKS) HOT 4
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