The wonderland of reflections
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10383370" target="_blank" >RIV/00216208:11320/18:10383370 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s11856-017-1621-9" target="_blank" >https://doi.org/10.1007/s11856-017-1621-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11856-017-1621-9" target="_blank" >10.1007/s11856-017-1621-9</a>
Alternative languages
Result language
angličtina
Original language name
The wonderland of reflections
Original language description
A fundamental fact for the algebraic theory of constraint satisfaction problems (CSPs) over a fixed template is that pp-interpretations between at most countable omega-categorical relational structures have two algebraic counterparts for their polymorphism clones: a semantic one via the standard algebraic operators H, S, P, and a syntactic one via clone homomorphisms (capturing identities). We provide a similar characterization which incorporates all relational constructions relevant for CSPs, that is, homomorphic equivalence and adding singletons to cores in addition to ppinterpretations. For the semantic part we introduce a new construction, called reflection, and for the syntactic part we find an appropriate weakening of clone homomorphisms, called h1 clone homomorphisms (capturing identities of height 1). As a consequence, the complexity of the CSP of an at most countable omega-categorical structure depends only on the identities of height 1 satisfied in its polymorphism clone as well as the natural uniformity thereon. This allows us in turn to formulate a new elegant dichotomy conjecture for the CSPs of reducts of finitely bounded homogeneous structures. Finally, we reveal a close connection between h1 clone homomorphisms and the notion of compatibility with projections used in the study of the lattice of interpretability types of varieties.
Czech name
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Czech description
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Classification
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
Result continuities
Project
<a href="/en/project/GA13-01832S" target="_blank" >GA13-01832S: General algebra and its connections to computer science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Israel Journal of Mathematics
ISSN
0021-2172
e-ISSN
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Volume of the periodical
223
Issue of the periodical within the volume
1
Country of publishing house
IL - THE STATE OF ISRAEL
Number of pages
36
Pages from-to
363-398
UT code for WoS article
000427197200011
EID of the result in the Scopus database
2-s2.0-85035759181