A term-generated model is a structure in which every element is the value of a closed term of the original language. Equivalently its substructure generated by the empty set, including interpretations of named constants, is the entire structure. This is the relevant meaning of “term model” for a model of an arbitrary complete theory, rather than a claim about one particular syntactic construction.
Each closed term gives the parameter-free defining formula . Thus
(1)
The next parts show that pointwise definability implies atomicity, and countable atomicity is equivalent to primeness. Therefore property (i) implies all three other properties.

Ancestors (14)

  1. i
  2. a
  3. 5
  4. B
  5. 2010
  6. Past exam of the model theory and Gödel's incompleteness theorems course of the University of Oxford
  7. Model theory and Gödel's incompleteness theorems course of the University of Oxford
  8. Year 4 of the mathematics course of the University of Oxford
  9. Mathematics course of the University of Oxford
  10. Undergraduate course of the University of Oxford
  11. Course of the University of Oxford
  12. University of Oxford
  13. List of universities
  14. Home

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