Set theory and Foundations of Mathematics1. First foundations of mathematicsThe last updated version is as the below list of separate html pages and also all in 1 html page.Previous versions in PDF (13 pages for main text + 7 pages for philosophical aspects). Some pages focus on model theory, others focus on set theory, others are philosophical 

1.1. Introduction to the foundations of mathematics 
What is mathematics Theories Foundations and developments Platonism vs Formalism The cycle of foundations 
1.2. Variables, sets, functions and operations  Constants Free and bound variables Ranges and sets Functions Operations 
1.3. Form of theories 
The variability of the model Notions and objects Onemodel theory The diversity of logical frameworks Examples of notions from various theories Metaobjects Components of theories Settheoretical interpretation 
1.4. Structures of mathematical systems  Firstorder structures Structures of set theory About of ZF set theory Formalizing types and structures as objects of onemodel theory 
1.5. Expressions and definable structures 
Terms and formulas Display conventions Variable structures Structures defined by expressions Invariant structures 
1.6. Logical connectives  Tautologies Negation Conjunctions, disjunctions Implication Chains of implications and equivalences 
1.7. Classes in set theory  Classes, sets and metasets Definiteness classes Extended definiteness 
1.8. Binders in set theory  The syntax of
binders setbuilder Russell's Paradox The function definer Relations 
1.9. Axioms and proofs  Statements Realistic vs. axiomatic theories in mathematics and other sciences Provability Logical validity Refutability and consistency 
1.10. Quantifiers  The quantifiers ∃,∀ Inclusion between classes Rules of proofs for quantifiers Completeness of firstorder logic 
1.11. Secondorder universal quantifiers  Secondorder quantification Secondorder Universal Introduction Secondorder Universal Elimination Incompleteness of secondorder logic Axioms of equality Defining new binders 
1.A. Time in model theory  The time of interpretation The metaphor of the usual time The infinite time between models The main foundational theories 
1.B. Introduction to incompleteness 
Truth undefinability The hierarchy of formulas : existence and provability Incompleteness theorems 
1.C. Set theory as a unified framework  Structure definers in diverse theories The unified framework of theories Set theory as a unified framework of itself Zeno's Paradox 
2. Set theory  
3. Algebra 4. Arithmetic 5. Secondorder foundations 
Other languages :
FR : ThÃ©orie des ensembles et fondement des mathÃ©matiques : Premiers fondements