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domain_of_discourse [2015/10/10 13:09] nikolaj |
domain_of_discourse [2015/10/10 14:15] nikolaj |
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| ===== Domain of discourse ===== | ===== Domain of discourse ===== | ||
| ==== Meta ==== | ==== Meta ==== | ||
| - | The following types form the primitive notions which, in this wiki, are not formally defined in terms of other concepts. | + | I also use the following types to classify the bulk of other entries in the wiki and these are the entries with formal content. |
| - | Nevertheless, their possible axiomatics are discussed in entries of type **Framework**. | + | |
| - | * ${\mathfrak D}_\mathrm{Propositions}$ ... [[Propositions]] | ||
| * ${\mathfrak D}_\mathrm{Sets}$ ... [[Sets]] | * ${\mathfrak D}_\mathrm{Sets}$ ... [[Sets]] | ||
| * ${\mathfrak D}_{\to}$ ... [[Functions]] | * ${\mathfrak D}_{\to}$ ... [[Functions]] | ||
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| * ${\mathfrak D}_\mathrm{Collections}$ ... [[Collections]], ad hoc subclasses of the above sorts (I use this as in some sort of naive set theory) | * ${\mathfrak D}_\mathrm{Collections}$ ... [[Collections]], ad hoc subclasses of the above sorts (I use this as in some sort of naive set theory) | ||
| - | I also use those to classify the bulk of other entries in the wiki. | + | The domains themselves are primitive notions. |
| - | There are also a minority of entries of type **Type**, as in //type theory//. They need not be part of the above framework. | + | Usage and axiomatics of those domains are discussed in entries of type **Framework**. |
| All **Set** entry definitions are purposely free from terms of the other domains, except for functions and tuples of sets (though tuples and also the functions we consider can just as well be modeled within a set theory, so that's just for clarity.). In this way, the set entries in this wiki can e.g. be interpreted as defining object within formal ZFC. | All **Set** entry definitions are purposely free from terms of the other domains, except for functions and tuples of sets (though tuples and also the functions we consider can just as well be modeled within a set theory, so that's just for clarity.). In this way, the set entries in this wiki can e.g. be interpreted as defining object within formal ZFC. | ||
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| + | There are also entries of type **Type**. The discussion of //type theories// in this wiki does not overlap with the above notions. | ||
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