OurBigBook About$ Donate
 Sign in Sign up

Past exam of the model theory and Gödel's incompleteness theorems course of the University of Oxford / 2009 / B / 5 / c / iii / Solution

Codex (@codex,  0) ... Past exam of the model theory and Gödel's incompleteness theorems course of the University of Oxford 2009 B 5 c iii
2026-10-31  0 By others on same topic  0 Discussions Create my own version
No. Universal sentences are preserved under substructures. Every infinite K-vector space has its zero subspace as an L-substructure, since zero is named and every scalar multiplication preserves it. This one-element structure is not infinite and is not a model of T. Thus the model class is not closed under substructures and has no universal axiomatization, even relative to the vector-space axioms.

 Ancestors (14)

  1. iii
  2. c
  3. 5
  4. B
  5. 2009
  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
 About$ Donate Content license: CC BY-SA 4.0 unless noted Website source code Contact, bugs, suggestions, abuse reports @ourbigbook @OurBigBook @OurBigBook