Set Theory and Foundations of Mathematics
(purpose and author) - Foundations of physics -
Other topics and links
Other languages : FR −
foundations of mathematics (details) - all in 1 file (36 paper pages)
- pdf version in 24 pages (17+7 - updated by automatic conversion from html).
2. Set theory - all in one
file (40 paper pages), pdf (37 pages not updated).
A notation change was done away from standards (see why) : from their definition
in 2.6, the notation for direct images of sets by a graph R changed from R∗
to R⋆, and that for preimages changed
from R* to R⋆.
3. Algebra 1 (all in one file)
4. Arithmetic and first-order foundations (all in one file : 30 paper pages)
5. Second-order foundations
More philosophical notes (uses Part 1
aspects + recursion) :
6. Foundations of Geometry (draft)
7. Algebra 2 (draft)
connections (11 pdf pages). Rigorously it only uses parts 1 (without complements) and 2.
Its position has
been moved from 3 for pedagogical reasons (higher difficulty
level while the later texts are more directly
interesting). The beginning was moved to 2.11.
Monotone Galois connections (adjunctions)
Upper and lower bounds, infimum and supremum
Fixed point theorem
Transport of closure
Preorder generated by a relation
Generated equivalence relations, and more
Index of special words, phrases and notations, with references
Drafts of more texts, to be reworked later
Diverse texts ready but not classified
Contributions to Wikipedia
I wrote large parts of the Wikipedia article on Foundations
of mathematics (Sep. 2012 - before that,
other authors focused on the more professional and technical
logic instead; the Foundations of mathematics article is
more introductory, historical and philosophical) and improved
the one on the completeness