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Model theory is the branch of mathematical logic which deals with the connection between a formal language and its interpretations, or models.

5 votes
1 answer
949 views

Elementary end extension of a countable model for ZF

Theorem 2.2.18 in Chang and Kiesler uses omitting types to show that any countable model of ZF has an elementary end extension. Can we control the countable order type of such a model? for example, if …
Eran's user avatar
  • 639
12 votes
7 answers
3k views

Use of indiscernibles in model theory

What is the main use of indiscernibles in model theory? reading through Chang and Keisler's Model Theory it seems that the main motivation for indicernibles is for getting many non-isomorphic models f …
Eran's user avatar
  • 639
6 votes
7 answers
5k views

Compactness Theorem for First Order Logic

Hi all, I am interested in proofs without using Goedel's completeness theorem. Does anyone have a reference to a proof of this theorem that uses Skolem Functions? How come Enderton's (Introduction t …
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  • 639