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. 

1.1. Introduction
to the foundations of mathematics
Mathematics and theories Foundations and developments The cycle of foundations 
Philosophical
aspects
(Each subsection assumes those on its left and top) Intuitive representation and abstraction
Platonism vs Formalism 
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 On the diversity of formalisms Examples of notions from various theories Metaobjects Components of theories 
Realistic vs. axiomatic theories in
mathematics and other sciences 
1.4. Structures of mathematical systems
Settheoretical interpretation 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
Variable structures Structures defined by expressions Invariant structures The role of axioms 
Time in model theory
The time of interpretation
The metaphor of the usual time The infinite time between models 
1.6. Logical connectives
Negation
1.7. Classes in set
theory Conjunctions, disjunctions Implication Chains of implications and equivalences Provability The unified framework of theories
Classes, sets and metasets 
Truth
undefinability The Berry paradox Zeno's Paradox 
Definiteness classes 1.8. Binders in set theoryExtended definiteness The syntax of
binders
Definition of functions by terms Relations and setbuilder symbol Russell's Paradox 
Time in set theory
The expansion of the set
theoretical universe
Can a set contain itself ? 
1.9. Quantifiers
The quantifiers ∃,∀
Inclusion between classes Rules of proofs for quantifiers Secondorder quantification Axioms of equality 
The relative sense of open quantifiers
Interpretation
of classesClasses in an expanding universe
Concrete examples 
1.10. Formalization
of set theory
The role of axioms
1.11. Set
generation principle
Open quantifiers, formulas vs statements Converting binders Axioms for notions The inclusion predicate Axioms for functions Criterion to accept some classes as sets :
Subsets, union, image, ⌀, pairs A general principle for the formalization of set theory Formalization of operations and currying 
Justifying the set
generation principle Concepts of truth in mathematics Provability
Arithmetic truths Set theoretical truths Alternative logical frameworks 
Other languages :
FR : Théorie des ensembles et fondement des mathématiques : Premiers fondements