Model Theory

模块目标

Build models from syntactic data and transfer properties along elementary maps, keeping language and theory distinct.

课程大纲

1. 01 Languages and structures 20h

   学习结果 Interpret a language in a structure and evaluate a formula.

   形成性检查 四选一检查

2. 02 Theories and satisfaction 25h

   学习结果 Separate a theory from one of its models; give two non-isomorphic models of the same theory if the syllabus example allows.

   形成性检查 反例

3. 03 Compactness 25h

   学习结果 Apply compactness to obtain a model of an infinite theory from finite fragments.

   形成性检查 书面推导

4. 04 Löwenheim–Skolem (taught grain) 20h

   学习结果 State a downward or upward form with cardinality hypotheses.

   形成性检查 四选一检查

5. 05 Elementary maps 25h

   学习结果 Check elementarity on a small example and say what isomorphism would add.

   形成性检查 书面推导

6. 06 Synthesis 35h

   学习结果 Write one compactness-plus-structure argument with the language named.

   形成性检查 书面推导

学习结果

Define a structure for a language, check a theory’s axioms in an example, and apply compactness or Löwenheim–Skolem at synopsis grain.

学科技能

Languages, structures, elementary equivalence, compactness, types at taught grain.

可迁移技能

Keep syntax and semantics labelled; do not treat a single model as the theory.