Axiom of Choice and Continuum Hypothesis - Connections and Differences

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F23%3A10493359" target="_blank" >RIV/00216208:11210/23:10493359 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ySPi50e.Hq" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ySPi50e.Hq</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.46938/tv.2022.546" target="_blank" >10.46938/tv.2022.546</a>

Jazyk výsledku

čeština

Název v původním jazyce

Axiom of Choice and Continuum Hypothesis - Connections and Differences

Popis výsledku v původním jazyce

We compare two well-known set-theoretical statements, namely the axiom of choice and the continuum hypothesis, with regard to their historical development and formulation, as well as their consequences in mathematics. It is known that both statements are independent from the other axioms of set theory (if they are consistent). The axiom of choice - despite initial controversies - is today almost universally accepted as an axiom. However, the status of the continuum hypothesis is more complex and no agreement has been found so far: both the continuum hypothesis and its negation (often as consequences of stronger statements) decide several mathematical problems differently, but in contrast with the axiom of choice it is not clear which of the two solutions should be the &quot;correct&quot; one (in the sense of an agreement within the community).

Název v anglickém jazyce

Axiom of Choice and Continuum Hypothesis - Connections and Differences

Popis výsledku anglicky

We compare two well-known set-theoretical statements, namely the axiom of choice and the continuum hypothesis, with regard to their historical development and formulation, as well as their consequences in mathematics. It is known that both statements are independent from the other axioms of set theory (if they are consistent). The axiom of choice - despite initial controversies - is today almost universally accepted as an axiom. However, the status of the continuum hypothesis is more complex and no agreement has been found so far: both the continuum hypothesis and its negation (often as consequences of stronger statements) decide several mathematical problems differently, but in contrast with the axiom of choice it is not clear which of the two solutions should be the &quot;correct&quot; one (in the sense of an agreement within the community).

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

60301 - Philosophy, History and Philosophy of science and technology

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Teorie vědy / Theory of Science

ISSN

1210-0250

e-ISSN

1804-6347

Svazek periodika

45

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

27

Strana od-do

67-93

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85163991821