4. Arithmetic and first-order foundations

4.1. Algebraic terms 4.2. Quotient systems 4.3. Term algebras 4.4. Integers and recursion
The set ℕ
Recursively defined sequences
Addition
Inversed recursion and integers
Multiplication
4.5. Presburger Arithmetic
4.6. Finiteness
4.7. Countability and Completeness 4.8. More recursion tools 4.9. Non-standard models of Arithmetic
Standard and non-standard numbers
Existence of non-standard models
Non-standard models of bare arithmetic
Non-standard models of Presburger Arithmetic
Non-standard models of full first-order arithmetic
4.11. Developing theories : definitions
Development levels : proofs, definitions, constructions
The Galois connection (Mod,Tru)
Schemes of definitions
Extending models by undefined structures
Definitions extend models
Definitions preserve sets of isomorphisms
4.9. Constructions
Construction schemes
A development scheme at each level looks like a component at the next level
How constructions preserve isomorphisms
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