Editing Model Theory (section)

== <span style="color: #FFFFFF;">Analyzing</span> ==
{| class="wikitable"
|+ Proof Theory vs. Model Theory
! Feature !! Proof Theory (Syntax) !! Model Theory (Semantics)
|-
| Focus || The rules of the language || The objects being talked about
|-
| Tool || Proof Trees / Inference Rules || Sets / Mappings / Ultraproducts
|-
| Goal || To show what is 'Provable' || To show what is 'Possible'
|-
| Analogy || The Grammar of a sentence || The Meaning of a sentence
|}

'''The Concept of "Definability"''': A set is "Definable" in a model if you can write a formula that describes exactly that set and nothing else. Model theorists analyze which sets are "Invisible" to certain languages. For example, in the language of addition, you can define "Even numbers," but in some languages, you can't. Analyzing "What can be said" is a core task of model theory.
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