Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics

Abstract In the context of implicational tonoid logics, this paper investigates analogues of Birkhoff’s two theorems, the so-called subdirect representation and varieties theorems, and of Mal’cev’s quasi-varieties theorem. More precisely, we first recall the class of implicational tonoid logics. Nex...
Ausführliche Beschreibung

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Autor*in:	Yang, Eunsuk [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Implicational tonoid logics Implicational tonoid matrices Subdirect representation Variety Quasi-variety

Anmerkung:	© Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Übergeordnetes Werk:	Enthalten in: Studia logica - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1953, 111(2023), 3 vom: 31. Jan., Seite 501-519
Übergeordnetes Werk:	volume:111 ; year:2023 ; number:3 ; day:31 ; month:01 ; pages:501-519

Links:	Volltext

DOI / URN:	10.1007/s11225-023-10035-8

Katalog-ID:	SPR051567938

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520			\|a Abstract In the context of implicational tonoid logics, this paper investigates analogues of Birkhoff’s two theorems, the so-called subdirect representation and varieties theorems, and of Mal’cev’s quasi-varieties theorem. More precisely, we first recall the class of implicational tonoid logics. Next, we establish the subdirect product representation theorem for those logics and then consider some more related results such as completeness. Thirdly, we consider the varieties theorem for them. Finally, we introduce an analogue of Mal’cev’s quasi-varieties theorem for algebras.
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allfields	10.1007/s11225-023-10035-8 doi (DE-627)SPR051567938 (SPR)s11225-023-10035-8-e DE-627 ger DE-627 rakwb eng Yang, Eunsuk verfasserin aut Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In the context of implicational tonoid logics, this paper investigates analogues of Birkhoff’s two theorems, the so-called subdirect representation and varieties theorems, and of Mal’cev’s quasi-varieties theorem. More precisely, we first recall the class of implicational tonoid logics. Next, we establish the subdirect product representation theorem for those logics and then consider some more related results such as completeness. Thirdly, we consider the varieties theorem for them. Finally, we introduce an analogue of Mal’cev’s quasi-varieties theorem for algebras. Implicational tonoid logics (dpeaa)DE-He213 Implicational tonoid matrices (dpeaa)DE-He213 Subdirect representation (dpeaa)DE-He213 Variety (dpeaa)DE-He213 Quasi-variety (dpeaa)DE-He213 Enthalten in Studia logica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1953 111(2023), 3 vom: 31. Jan., Seite 501-519 (DE-627)271175788 (DE-600)1478982-6 1572-8730 nnns volume:111 year:2023 number:3 day:31 month:01 pages:501-519 https://dx.doi.org/10.1007/s11225-023-10035-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2938 GBV_ILN_2947 GBV_ILN_2949 GBV_ILN_2950 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 AR 111 2023 3 31 01 501-519
spelling	10.1007/s11225-023-10035-8 doi (DE-627)SPR051567938 (SPR)s11225-023-10035-8-e DE-627 ger DE-627 rakwb eng Yang, Eunsuk verfasserin aut Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In the context of implicational tonoid logics, this paper investigates analogues of Birkhoff’s two theorems, the so-called subdirect representation and varieties theorems, and of Mal’cev’s quasi-varieties theorem. More precisely, we first recall the class of implicational tonoid logics. Next, we establish the subdirect product representation theorem for those logics and then consider some more related results such as completeness. Thirdly, we consider the varieties theorem for them. Finally, we introduce an analogue of Mal’cev’s quasi-varieties theorem for algebras. Implicational tonoid logics (dpeaa)DE-He213 Implicational tonoid matrices (dpeaa)DE-He213 Subdirect representation (dpeaa)DE-He213 Variety (dpeaa)DE-He213 Quasi-variety (dpeaa)DE-He213 Enthalten in Studia logica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1953 111(2023), 3 vom: 31. Jan., Seite 501-519 (DE-627)271175788 (DE-600)1478982-6 1572-8730 nnns volume:111 year:2023 number:3 day:31 month:01 pages:501-519 https://dx.doi.org/10.1007/s11225-023-10035-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2938 GBV_ILN_2947 GBV_ILN_2949 GBV_ILN_2950 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 AR 111 2023 3 31 01 501-519
allfields_unstemmed	10.1007/s11225-023-10035-8 doi (DE-627)SPR051567938 (SPR)s11225-023-10035-8-e DE-627 ger DE-627 rakwb eng Yang, Eunsuk verfasserin aut Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In the context of implicational tonoid logics, this paper investigates analogues of Birkhoff’s two theorems, the so-called subdirect representation and varieties theorems, and of Mal’cev’s quasi-varieties theorem. More precisely, we first recall the class of implicational tonoid logics. Next, we establish the subdirect product representation theorem for those logics and then consider some more related results such as completeness. Thirdly, we consider the varieties theorem for them. Finally, we introduce an analogue of Mal’cev’s quasi-varieties theorem for algebras. Implicational tonoid logics (dpeaa)DE-He213 Implicational tonoid matrices (dpeaa)DE-He213 Subdirect representation (dpeaa)DE-He213 Variety (dpeaa)DE-He213 Quasi-variety (dpeaa)DE-He213 Enthalten in Studia logica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1953 111(2023), 3 vom: 31. Jan., Seite 501-519 (DE-627)271175788 (DE-600)1478982-6 1572-8730 nnns volume:111 year:2023 number:3 day:31 month:01 pages:501-519 https://dx.doi.org/10.1007/s11225-023-10035-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2938 GBV_ILN_2947 GBV_ILN_2949 GBV_ILN_2950 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 AR 111 2023 3 31 01 501-519
allfieldsGer	10.1007/s11225-023-10035-8 doi (DE-627)SPR051567938 (SPR)s11225-023-10035-8-e DE-627 ger DE-627 rakwb eng Yang, Eunsuk verfasserin aut Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In the context of implicational tonoid logics, this paper investigates analogues of Birkhoff’s two theorems, the so-called subdirect representation and varieties theorems, and of Mal’cev’s quasi-varieties theorem. More precisely, we first recall the class of implicational tonoid logics. Next, we establish the subdirect product representation theorem for those logics and then consider some more related results such as completeness. Thirdly, we consider the varieties theorem for them. Finally, we introduce an analogue of Mal’cev’s quasi-varieties theorem for algebras. Implicational tonoid logics (dpeaa)DE-He213 Implicational tonoid matrices (dpeaa)DE-He213 Subdirect representation (dpeaa)DE-He213 Variety (dpeaa)DE-He213 Quasi-variety (dpeaa)DE-He213 Enthalten in Studia logica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1953 111(2023), 3 vom: 31. Jan., Seite 501-519 (DE-627)271175788 (DE-600)1478982-6 1572-8730 nnns volume:111 year:2023 number:3 day:31 month:01 pages:501-519 https://dx.doi.org/10.1007/s11225-023-10035-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2938 GBV_ILN_2947 GBV_ILN_2949 GBV_ILN_2950 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 AR 111 2023 3 31 01 501-519
allfieldsSound	10.1007/s11225-023-10035-8 doi (DE-627)SPR051567938 (SPR)s11225-023-10035-8-e DE-627 ger DE-627 rakwb eng Yang, Eunsuk verfasserin aut Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In the context of implicational tonoid logics, this paper investigates analogues of Birkhoff’s two theorems, the so-called subdirect representation and varieties theorems, and of Mal’cev’s quasi-varieties theorem. More precisely, we first recall the class of implicational tonoid logics. Next, we establish the subdirect product representation theorem for those logics and then consider some more related results such as completeness. Thirdly, we consider the varieties theorem for them. Finally, we introduce an analogue of Mal’cev’s quasi-varieties theorem for algebras. Implicational tonoid logics (dpeaa)DE-He213 Implicational tonoid matrices (dpeaa)DE-He213 Subdirect representation (dpeaa)DE-He213 Variety (dpeaa)DE-He213 Quasi-variety (dpeaa)DE-He213 Enthalten in Studia logica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1953 111(2023), 3 vom: 31. Jan., Seite 501-519 (DE-627)271175788 (DE-600)1478982-6 1572-8730 nnns volume:111 year:2023 number:3 day:31 month:01 pages:501-519 https://dx.doi.org/10.1007/s11225-023-10035-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2938 GBV_ILN_2947 GBV_ILN_2949 GBV_ILN_2950 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 AR 111 2023 3 31 01 501-519
language	English
source	Enthalten in Studia logica 111(2023), 3 vom: 31. Jan., Seite 501-519 volume:111 year:2023 number:3 day:31 month:01 pages:501-519
sourceStr	Enthalten in Studia logica 111(2023), 3 vom: 31. Jan., Seite 501-519 volume:111 year:2023 number:3 day:31 month:01 pages:501-519
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topic_facet	Implicational tonoid logics Implicational tonoid matrices Subdirect representation Variety Quasi-variety
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container_title	Studia logica
authorswithroles_txt_mv	Yang, Eunsuk @@aut@@
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author	Yang, Eunsuk
spellingShingle	Yang, Eunsuk misc Implicational tonoid logics misc Implicational tonoid matrices misc Subdirect representation misc Variety misc Quasi-variety Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics
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topic_title	Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics Implicational tonoid logics (dpeaa)DE-He213 Implicational tonoid matrices (dpeaa)DE-He213 Subdirect representation (dpeaa)DE-He213 Variety (dpeaa)DE-He213 Quasi-variety (dpeaa)DE-He213
topic	misc Implicational tonoid logics misc Implicational tonoid matrices misc Subdirect representation misc Variety misc Quasi-variety
topic_unstemmed	misc Implicational tonoid logics misc Implicational tonoid matrices misc Subdirect representation misc Variety misc Quasi-variety
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title	Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics
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title_full	Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics
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title_sort	birkhoff’s and mal’cev’s theorems for implicational tonoid logics
title_auth	Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics
abstract	Abstract In the context of implicational tonoid logics, this paper investigates analogues of Birkhoff’s two theorems, the so-called subdirect representation and varieties theorems, and of Mal’cev’s quasi-varieties theorem. More precisely, we first recall the class of implicational tonoid logics. Next, we establish the subdirect product representation theorem for those logics and then consider some more related results such as completeness. Thirdly, we consider the varieties theorem for them. Finally, we introduce an analogue of Mal’cev’s quasi-varieties theorem for algebras. © Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstractGer	Abstract In the context of implicational tonoid logics, this paper investigates analogues of Birkhoff’s two theorems, the so-called subdirect representation and varieties theorems, and of Mal’cev’s quasi-varieties theorem. More precisely, we first recall the class of implicational tonoid logics. Next, we establish the subdirect product representation theorem for those logics and then consider some more related results such as completeness. Thirdly, we consider the varieties theorem for them. Finally, we introduce an analogue of Mal’cev’s quasi-varieties theorem for algebras. © Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstract_unstemmed	Abstract In the context of implicational tonoid logics, this paper investigates analogues of Birkhoff’s two theorems, the so-called subdirect representation and varieties theorems, and of Mal’cev’s quasi-varieties theorem. More precisely, we first recall the class of implicational tonoid logics. Next, we establish the subdirect product representation theorem for those logics and then consider some more related results such as completeness. Thirdly, we consider the varieties theorem for them. Finally, we introduce an analogue of Mal’cev’s quasi-varieties theorem for algebras. © Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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title_short	Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics
url	https://dx.doi.org/10.1007/s11225-023-10035-8
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doi_str	10.1007/s11225-023-10035-8
up_date	2024-07-03T22:34:01.781Z
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score	7.398121

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Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics

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