Epimorphisms, Definability and Cardinalities

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F20%3A00503853" target="_blank" >RIV/67985807:_____/20:00503853 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11225-019-09846-5" target="_blank" >http://dx.doi.org/10.1007/s11225-019-09846-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11225-019-09846-5" target="_blank" >10.1007/s11225-019-09846-5</a>

Result language
angličtina
Original language name
Epimorphisms, Definability and Cardinalities
Original language description
We characterize, in syntactic terms, the ranges of epimorphisms in an arbitrary class of similar first-order structures (as opposed to an elementary class). This allows us to strengthen a result of Bacsich, as follows: in any prevariety having at most s nonlogical symbols and an axiomatization requiring at most m variables, if the epimorphisms into structures with at most m + s + ℵ0 elements are surjective, then so are all of the epimorphisms. Using these facts, we formulate and prove manageable 'bridge theorems', matching the surjectivity of all epimorphisms in the algebraic counterpart of a logic ⊢ with suitable infinitary definability properties of ⊢ , while not making the standard but awkward assumption that ⊢ comes furnished with a proper class of variables.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-04630S" target="_blank" >GA17-04630S: Predicate graded logics and their applications to computer science</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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