A basis of a pregeometry is a maximal independent set. Every element lies in the closure of a basis, and the exchange property implies that all bases have the same cardinality.
The dimension of a closed set over a smaller closed set is the cardinality of any basis of the larger set over the smaller one. The exchange property makes this cardinality independent of the chosen basis.

Ancestors (8)

  1. Pregeometry
  2. Model-theoretic algebraic closure
  3. Strongly minimal theory
  4. Model theory
  5. Foundations of mathematics
  6. Area of mathematics
  7. Mathematics
  8. Home

Incoming links (1)

View article source

Discussion (0)

New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version