Finite Sets and Natural Numbers
This course on set theory and finite structures is an attempt to better understand certain questions on the foundations of mathematics including Benacerraf's Identification Problem and Hilbert's 24-th Problem. A Canonical Set Theory is proposed for a simple and transparent construction of natural numbers. This set theory also gives new results that tie together set theory, finite mathematics, group theory, number theory and analysis.
Course Material
Video Lectures
Course Notes
Supplementary Material
The supplementary material includes examples, problem sets, extra topics, detailed proofs and external references to complementary books, videos, reviews, essays and more.
Examples and Problem Sets
Bibliography
Additional Links
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“The Nature of Numbers”. Logic and Foundations Special Session, 52 Mexican Congress of Mathematics, Monterrey, Nuevo León, 2019. (Click here for VIDEO)
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“Simple Representation of Natural and Real Numbers”. Logic and Foundations Special Sessions, 55 Mexican Congress of Mathematics, Guadalajara, Jalisco, 2022. (Click here for VIDEO)
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"A Pseudo Measure on the Space of Finite Functions and Permutations”. Algebra Special Sessions, 56 Mexican Congress of Mathematics, San Luis Potosí, 2023. (Click here for VIDEO)
