On Equality and Natural Numbers in Cantor-Lukasiewicz Set Theory

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F13%3A00343863" target="_blank" >RIV/67985807:_____/13:00343863 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1093/jigpal/jzq019" target="_blank" >http://dx.doi.org/10.1093/jigpal/jzq019</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/jigpal/jzq019" target="_blank" >10.1093/jigpal/jzq019</a>

Result language
angličtina
Original language name
On Equality and Natural Numbers in Cantor-Lukasiewicz Set Theory
Original language description
Two equality predicates in Cantor-Lukasiewicz set theory (with full comprehension, over Lukasiewicz predicate logic) are investigated: extensional =e and Leibniz equality =. It is proved that there are many pairs of sets x,y such that x =e y & x =/= y istrue. In particular, x may be the set omega of natural numbers, defined together with ternary predicates for addition and multiplication. The main result says that the Cantor-Lukasiewicz set theory is essentially undecidable and essentially incomplete.The proof is difficult since it is not supposed that the set omega is crisp (non-fuzzy).
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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