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domain_of_discourse [2015/10/10 13:45] nikolaj |
domain_of_discourse [2015/10/10 14:15] nikolaj |
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| I also use the following types to classify the bulk of other entries in the wiki and these are the entries with formal content. | I also use the following types to classify the bulk of other entries in the wiki and these are the entries with formal content. | ||
| - | * ${\mathfrak D}_\mathrm{Propositions}$ ... [[Propositions]] | ||
| * ${\mathfrak D}_\mathrm{Sets}$ ... [[Sets]] | * ${\mathfrak D}_\mathrm{Sets}$ ... [[Sets]] | ||
| * ${\mathfrak D}_{\to}$ ... [[Functions]] | * ${\mathfrak D}_{\to}$ ... [[Functions]] | ||
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| The domains themselves are primitive notions. | The domains themselves are primitive notions. | ||
| Usage and axiomatics of those domains are discussed in entries of type **Framework**. | Usage and axiomatics of those domains are discussed in entries of type **Framework**. | ||
| - | There are also a minority of entries of type **Type**, as in //type theory//. They need not be part of the above 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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