집합론,set_theory

Difference between r1.48 and the current

@@ -12,11 +12,11 @@
[[자연수의_분할,integer_partition]]

// 이 둘은 대비됨
소박한집합론 naive_set_theory https://proofwiki.org/wiki/Definition:Naive_Set_Theory [[WpEn:Naive_set_theory]] '''Naïve set theory'''
공리적집합론 axiomatic_set_theory https://proofwiki.org/wiki/Definition:Axiomatic_Set_Theory
소박한집합론 naive_set_theory https://proofwiki.org/wiki/Definition:Naive_Set_Theory [[WpEn:Naive_set_theory]] { '''naïve set theory / naive set theory''' Rel. WpKo:부랄리포르티_역설 } // "naive set theory" Ggl:"naive set theory"
공리적집합론 axiomatic_set_theory https://proofwiki.org/wiki/Definition:Axiomatic_Set_Theory { mkl [[공리,axiom]] }

// 이 둘도 대비됨.
structural_set_theory https://ncatlab.org/nlab/show/structural+set+theory ..... 구조적집합론? 구조집합론?
structural_set_theory https://ncatlab.org/nlab/show/structural+set+theory ..... 구조적집합론? 구조집합론? { mkl [[구조,structure]] }
zeroth-order_set_theory https://ncatlab.org/nlab/show/zeroth-order+set+theory
first-order_set_theory https://ncatlab.org/nlab/show/first-order+set+theory
higher-order_set_theory https://ncatlab.org/nlab/show/higher-order+set+theory
@@ -66,6 +66,13 @@
[[WpEn:von_Neumann–Bernays–Gödel_set_theory]]
[[WpJa:フォン・ノイマン＝ベルナイス＝ゲーデル集合論]]
... Ndict:nbg+set+theory Ggl:nbg+set+theory
set_theoretic_programming
'''set theoretic programming'''
집합론적 프로그래밍
[[WpEn:Set_theoretic_programming]]
Ggl:"set theoretic programming"
Up: [[집합론,set_theory]] [[프로그래밍패러다임,programming_paradigm]]

Related/MKL:
[[논리,logic]] esp [[수리논리,mathematical_logic]]
@@ -155,5 +162,4 @@
https://plato.stanford.edu/entries/set-theory/
[[Wiki:SetTheory]]
[[https://terms.naver.com/entry.naver?docId=3405344&cid=47324&categoryId=47324 수학백과 집합론]]


집합,set 이론

Up:
수학,math
집합과_확률,set_and_probability
집합,set 이론,theory

Sub:
// 분할,partition:
집합의_분할,set_partition
자연수의_분할,integer_partition

// 이 둘은 대비됨
소박한집합론 naive_set_theory https://proofwiki.org/wiki/Definition:Naive_Set_Theory WpEn:Naive_set_theory { naïve set theory / naive set theory Rel. WpKo:부랄리포르티_역설 } // "naive set theory" Ggl:naive set theory
공리적집합론 axiomatic_set_theory https://proofwiki.org/wiki/Definition:Axiomatic_Set_Theory { mkl 공리,axiom }

// 이 둘도 대비됨.
structural_set_theory https://ncatlab.org/nlab/show/structural set theory ..... 구조적집합론? 구조집합론? { mkl 구조,structure }
zeroth-order_set_theory https://ncatlab.org/nlab/show/zeroth-order set theory
first-order_set_theory https://ncatlab.org/nlab/show/first-order set theory
higher-order_set_theory https://ncatlab.org/nlab/show/higher-order set theory
material_set_theory
AKA membership-based set theory
ex. ZFC
sub - 순집합? 순수집합? ,pure_set https://ncatlab.org/nlab/show/pure set
https://ncatlab.org/nlab/show/material set theory
see also https://ncatlab.org/nlab/show/material-structural adjunction

descriptive_set_theory - 작성중
https://mathworld.wolfram.com/DescriptiveSetTheory.html

pure_set_theory pure set theory "is a system of set theory in which all elements of sets are themselves sets."(pw) https://proofwiki.org/wiki/Definition:Pure_Set_Theory

// 아래 MKL: axiomatic_set_theory

Z집합론 Zermelo_set_theory ? or Z_set_theory ?
Zermelo set theory
WpEn:Zermelo_set_theory = https://en.wikipedia.org/wiki/Zermelo_set_theory
https://plato.stanford.edu/entries/zermelo-set-theory/
"Zermelo set theory"
Ggl:Zermelo set theory
// Ernst_Zermelo { Ernst Zermelo WpEn:Ernst_Zermelo }
ZF집합론 ZF_set_theory ? or Zermelo-Fraenkel_set_theory ?
Zermelo-Fraenkel set theory
[https]수학백과 ZF 집합론
Libre:체르멜로-프렝켈_집합론
WpKo:체르멜로-프렝켈_집합론 = https://ko.wikipedia.org/wiki/체르멜로-프렝켈_집합론
WpSp:Zermelo–Fraenkel_set_theory = https://simple.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory
WpEn:Zermelo–Fraenkel_set_theory = https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory
WpJa:ツェルメロ＝フレンケル集合論 = https://ja.wikipedia.org/wiki/ツェルメロ＝フレンケル集合論
https://plato.stanford.edu/entries/set-theory/ZF.html
"Zermelo-Fraenkel set theory"
Ggl:Zermelo-Fraenkel set theory
// Abraham_Fraenkel { Abraham Fraenkel WpEn:Abraham_Fraenkel }

ZFC집합론 ZFC_set_theory
ZF set theory에 선택공리,choice_axiom{ https://encyclopediaofmath.org/wiki/Axiom_of_choice }만 추가한?
https://encyclopediaofmath.org/wiki/ZFC
https://ncatlab.org/nlab/show/ZFC

NBG집합론 NBG_set_theory
von Neumann–Bernays–Gödel set theory (NBG)
ZF의 확장,extension, esp conservative_extension { conservative extension WpKo:보존적_확장 WpEn:Conservative_extension Up: 보존,conservation 확장,extension }
[https]수학백과 NBG 집합론
WpEn:von_Neumann–Bernays–Gödel_set_theory
WpJa:フォン・ノイマン＝ベルナイス＝ゲーデル集合論
... Ndict:nbg set theory Ggl:nbg set theory

set_theoretic_programming
set theoretic programming
집합론적 프로그래밍
WpEn:Set_theoretic_programming
Ggl:set theoretic programming
Up: 집합론,set_theory 프로그래밍패러다임,programming_paradigm

Related/MKL:
논리,logic esp 수리논리,mathematical_logic
사건,event
수학기초론
foundations of mathematics
WpKo:수학기초론
WpEn:Foundations_of_mathematics
WpJa:数学基礎論
공리,axiom
axiom_system 공리계 maybe... or 공리체계
universe =,universe { 전체 .... KmsE:universe }
모형,model 모델,model


Topics:
reflection_principle - writing



[edit]

1. 연산


$\neg(p\wedge q)\Leftrightarrow \neg p \vee \neg q$
$\neg(p\vee q)\Leftrightarrow \neg p \wedge \neg q$
이것은 논리곱 ∧과 논리합 ∨사이의 쌍대성,duality.[1]

from (10개의 특강으로 끝내는 수학의 기본 원리)
{
$\sim(A\cup B)=(\sim A)\cap(\sim B)$ 합집합의 여집합은 여집합들의 교집합이다.
$\sim(A\cap B)=(\sim A)\cup(\sim B)$ 교집합의 여집합은 여집합들의 합집합이다.
}


[edit]

2. Bmks ko

계승혁 - 집합과 수리논리 강의 동영상 (2020)
https://www.math.snu.ac.kr/~kye/lecture_V/V_set/index.html

[edit]

3. Bmks en

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