Axiom of Choice and Continuum Hypothesis - Connections and Differences
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
čeština
Original language name
Axiom of Choice and Continuum Hypothesis - Connections and Differences
Original language description
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 "correct" one (in the sense of an agreement within the community).
Czech name
Axiom of Choice and Continuum Hypothesis - Connections and Differences
Czech description
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 "correct" one (in the sense of an agreement within the community).
Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
—
OECD FORD branch
60301 - Philosophy, History and Philosophy of science and technology
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Teorie vědy / Theory of Science
ISSN
1210-0250
e-ISSN
1804-6347
Volume of the periodical
45
Issue of the periodical within the volume
1
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
27
Pages from-to
67-93
UT code for WoS article
—
EID of the result in the Scopus database
2-s2.0-85163991821