純粋・応用数学・数学隣接分野（含むガロア理論）20

[過去ﾛｸﾞ] 純粋・応用数学・数学隣接分野（含むガロア理論）20 (1002ﾚｽ)
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195: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2025/05/09(金) 18:22:54.03 ID:bmPDK4UI

>>185 追加

ぶっはは、ぶっはは ；ｐ）

google検索:Real number axiom set theory pdf
結果見繕い
１）
The real numbers in inner models of set theory
Dipòsit Digital de la Universitat de Barcelona
https://diposit.ub.edu/dspace/bitstream/2445/196900/1/tfg_soto_quintanilla_martin.pdf
M Soto Quintanilla 著 · 2022 — Inner models are transitive set theoretic classes that satisfy the axioms of ZF and contain all the ordinals. That is, a smaller mathematical universe that ...
53 ページ

２）
https://web.math.ucsb.edu/~moore/2axiomsforreals.pdf
Math 117: Axioms for the Real Numbers
John Douglas Moore October 11, 2010
The last stage is developing the real numbers R, which can be thought of as limits of sequences of rational numbers.
For example is the limit of the sequence (3,3.1,3.14,3.141,3.1415,3.14159,3.141592,・・・,3,14159265358979・・・ )
It is precisely the notion of defining the limit of such a sequence which is the major difficulty in developing real analysis.
It would take a long time just to define the real numbers in this manner.

３）
https://faculty.uccs.edu/goman/wp-content/uploads/sites/15/2021/02/An-independent-axiom-system-for-the-real-numbers.pdf
VOL. 40, NO. 2, MARCH 2009 THE COLLEGE MATHEMATICSJOURNAL
An Independent Axiom System for the Real Numbers Greg Oman
Greg Oman is a visiting instructor at Otterbein College in Westerville, Ohio. He obtained his Ph.D. in 2006 from The Ohio State University, and currently works in several areas of mathematics including ring theory, semigroup theory, and logic. When not doing math, he enjoys working out, traveling, and playing with The Sweet.

４）
3 Axioms for the real number system
University of Notre Dame
https://www3.nd.edu/~dgalvin1/10860/10860_S20/book/Sec3.pdf
The approach we are going to take to understanding the real numbers will be axiomatic: we will write down a collection of axioms, that we should all agree that ...
30 ページ

５）
Axioms of Set Theory
ETH Zürich
https://people.math.ethz.ch/~halorenz/4students/LogikML/ZFC.pdf
W Axioms 著 — As an application of the CANTOR–BERNSTEIN THEOREM 3.14 let us show that the set of real numbers, denoted by R, has the same cardinality as 乡(ω).

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