Geometric and conditional geometric equivalences of algebras
The basis for classifying universal algebras is conventionally formed by one or other type of equivalence relations between the algebras, such as isomorphism, elementary equivalence, equivalence of algebras in different logical languages, geometric equivalence, and so on. Of crucial importance in th...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Pinus, A. G. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
geometrically equivalent algebras conditionally geometrically equivalent algebras |
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| Anmerkung: |
© Springer Science+Business Media New York 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Algebra and logic - Springer US, 1968, 51(2013), 6 vom: Jan., Seite 507-510 |
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| Übergeordnetes Werk: |
volume:51 ; year:2013 ; number:6 ; month:01 ; pages:507-510 |
| Links: |
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| DOI / URN: |
10.1007/s10469-013-9210-4 |
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OLC2071187121 |
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| 520 | |a The basis for classifying universal algebras is conventionally formed by one or other type of equivalence relations between the algebras, such as isomorphism, elementary equivalence, equivalence of algebras in different logical languages, geometric equivalence, and so on. Of crucial importance in this event are results that reduce one of such equivalences to another. The most important example (enjoying multiple applications) is the theorem stating that every two algebras are elementarily equivalent iff their ultrapowers with respect to some ultrafilters are isomorphic. Similar results are established for various equivalences of algebras related to algebraic geometry of universal algebras. | ||
| 650 | 4 | |a geometrically equivalent algebras | |
| 650 | 4 | |a conditionally geometrically equivalent algebras | |
| 650 | 4 | |a syntactically implicitly equivalent algebras | |
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10.1007/s10469-013-9210-4 doi (DE-627)OLC2071187121 (DE-He213)s10469-013-9210-4-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Pinus, A. G. verfasserin aut Geometric and conditional geometric equivalences of algebras 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 The basis for classifying universal algebras is conventionally formed by one or other type of equivalence relations between the algebras, such as isomorphism, elementary equivalence, equivalence of algebras in different logical languages, geometric equivalence, and so on. Of crucial importance in this event are results that reduce one of such equivalences to another. The most important example (enjoying multiple applications) is the theorem stating that every two algebras are elementarily equivalent iff their ultrapowers with respect to some ultrafilters are isomorphic. Similar results are established for various equivalences of algebras related to algebraic geometry of universal algebras. geometrically equivalent algebras conditionally geometrically equivalent algebras syntactically implicitly equivalent algebras ∞-quasiequational theory of algebras Enthalten in Algebra and logic Springer US, 1968 51(2013), 6 vom: Jan., Seite 507-510 (DE-627)129934453 (DE-600)390280-8 (DE-576)015492621 0002-5232 nnns volume:51 year:2013 number:6 month:01 pages:507-510 https://doi.org/10.1007/s10469-013-9210-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_2088 AR 51 2013 6 01 507-510 |
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The basis for classifying universal algebras is conventionally formed by one or other type of equivalence relations between the algebras, such as isomorphism, elementary equivalence, equivalence of algebras in different logical languages, geometric equivalence, and so on. Of crucial importance in this event are results that reduce one of such equivalences to another. The most important example (enjoying multiple applications) is the theorem stating that every two algebras are elementarily equivalent iff their ultrapowers with respect to some ultrafilters are isomorphic. Similar results are established for various equivalences of algebras related to algebraic geometry of universal algebras. © Springer Science+Business Media New York 2013 |
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The basis for classifying universal algebras is conventionally formed by one or other type of equivalence relations between the algebras, such as isomorphism, elementary equivalence, equivalence of algebras in different logical languages, geometric equivalence, and so on. Of crucial importance in this event are results that reduce one of such equivalences to another. The most important example (enjoying multiple applications) is the theorem stating that every two algebras are elementarily equivalent iff their ultrapowers with respect to some ultrafilters are isomorphic. Similar results are established for various equivalences of algebras related to algebraic geometry of universal algebras. © Springer Science+Business Media New York 2013 |
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The basis for classifying universal algebras is conventionally formed by one or other type of equivalence relations between the algebras, such as isomorphism, elementary equivalence, equivalence of algebras in different logical languages, geometric equivalence, and so on. Of crucial importance in this event are results that reduce one of such equivalences to another. The most important example (enjoying multiple applications) is the theorem stating that every two algebras are elementarily equivalent iff their ultrapowers with respect to some ultrafilters are isomorphic. Similar results are established for various equivalences of algebras related to algebraic geometry of universal algebras. © Springer Science+Business Media New York 2013 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2071187121</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230502195909.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2013 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10469-013-9210-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2071187121</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10469-013-9210-4-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Pinus, A. G.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Geometric and conditional geometric equivalences of algebras</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media New York 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The basis for classifying universal algebras is conventionally formed by one or other type of equivalence relations between the algebras, such as isomorphism, elementary equivalence, equivalence of algebras in different logical languages, geometric equivalence, and so on. Of crucial importance in this event are results that reduce one of such equivalences to another. The most important example (enjoying multiple applications) is the theorem stating that every two algebras are elementarily equivalent iff their ultrapowers with respect to some ultrafilters are isomorphic. 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