Survey 1979: Equational Logic - Department of Mathematics ...

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274. 275. 276. 277. Ferrara (7), 14(1969), 1-4. (14.8} , Idealizable varieties, J. Algebra, 26(1973), 152-165. , Classi e schemi ideali, Ann. Scuola Norm. Sup. Pisa, Classe Scienze, 27(1973), 687-706. { 14.7 } Makkai, M., Preservation theorems, J. Symbolic Logic, 34(1969), 437-459. {3} A proof of Baker's finite basis theorem, Algebra Universalis, 3(1973), 174-181.i 9.11} 278. Malcev, A. I., On the general theory of algebraic systems, (in Russian), Math. Sbornik (N.S.), (77), 35(1954), 3-20. English translation: Amer. Math. Soc. Transl. (2), 27(1963), 125-142. {15 } 279. __ , The metamathematics of algebraic systems, collected papers 1936-67, translated and edited by B. F. Wells III, North-Holland, Amsterdam, 1971. { 3,17.9, [281 ] } 280. __ , Algebraic systems, (translated from Russian by B. D. Seckler and A. P. Doohovskoy), Vol. 192 of Grundlehren der mathematischen Wissenschaften, Springer-Verlag, New York, 1973. {3 } 281. __ , Identical relations in varieties ofquasigroups, appears in [279]. {12} 282. Marczewski, E., Independence in abstract algebras - results and problems, Colloq. Math., 14(1966), 169-188. {7,14.5,15} 283. __ , Opening Address ibid, 357-359. {Introduction} 284. Margaris, A., Identities in implicative semilattices, Proc, Amer. Math. Soc., 41(1973), 443-448. { 12} 285. Markov, A. A., On the impossibility of certain algorithms in the theory of associative systems, Dokl. Akad. Nauk SSSR (N.S.), 55(1947), 587-590. Translation: Comptes Rendus URSS, 44(1947), 583-586. {12} 286. Martin, C. F., Equational theories of natural numbers and transJ?nite ordinals, Ph.D. Thesis, Berkeley, 1973.{8.10,8.11,8.12,8.13,9.20,9.21,12} 287. , Abstract, Notices Amer. Math. Soc., 17(1970), 638. { 9.20} 288. Martihez, J., Varieties of lattice-ordered groups, Math. Z., 137(1974), 265-284. { 13.10 } 289. Mazzanti, G., Classi ideali e distributivit delle congruenze, Ann. Univ. Ferrara (7), 19(1974), 145-156. {14.73 290. McKenzie, R., On the unique factorization problem for finite commutative semigroups, Notices Amer. Math. Soc., 12(1965), 315. 291. -- Equational bases for lattice theories, Math. Scand., 27(1970), 24-38. {6',9.10,9.19,10.1,10.8,10.9,13.11 } 292. , Definability in lattices of equational theories, Annals Math. Logic, 3(1971), 197-237.{13} 293. , lql-incompactness of Z, Colloq. Math., 23(1971), 199-202. 294. , A method for obtaining refinement theorems, with an application to semigroups, Algebra Universalis, 2(1972), 324-338. {14.10 } 295. , Equational bases and nonmodular lattice varieties, Trans. Amer. Math. Soc., 174(1972), 1-43. {13} 296. __ , On spectra, and the negative solution of the decision problem for identities having a finite non-trivial model, J. Symbolic Logic, 40(1975), 186-196. { 10.7,12.2,14.1,14.3} 297. , Abstract 731-20-47, Notices Amer. Math. Soc., 23(1976), A-93. {9.5} 298. , Some unresolved problems between lattice theory and equational logic, Proceedings of the 1973 Houston Lattice Theory Conference, 564-573. { 15} 299. , On minimal locally finite varieties with permuting congruence relations, Ms., Berkeley, 1976. { 9.12,9 } 63
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HOUSTON JOURNAL OF MATHEMATICS Surv
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EQUATIONAL LOGIC Walter Taylor This
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EQUATIONAL LOGIC CONTENTS 1. Early
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2 EQUATIONAL LOGIC 2. The existence
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4 EQUATIONAL LOGIC A are taken as v
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6 EQUATIONAL LOGIC is closed under
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8 EQUATIONAL LOGIC model theory, an
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10 EQUATIONAL LOGIC completeness th
Page 17 and 18: 12 EQUATIONAL LOGIC algebras do not
Page 19 and 20: 14 EQUATIONAL LOGIC groups with a s
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Page 23 and 24: 18 EQUATIONAL LOGIC algebras A with
Page 25 and 26: 20 EQUATIONAL LOGIC 9.18. Some vari
Page 27 and 28: 22 EQUATIONAL LOGIC some algebras o
Page 29 and 30: 24 EQUATIONAL LOGIC is an interval
Page 31 and 32: 26 EQUATIONAL LOGIC The second meth
Page 33 and 34: 28 EQUATIONAL LOGIC for arbitrary f
Page 35 and 36: 30 EQUATIONAL LOGIC The theory Z 1
Page 37 and 38: 32 EQUATIONAL LOGIC conversely, eve
Page 39 and 40: 34 EQUATIONAL LOGIC x=y Boolean alc
Page 41 and 42: 36 EQUATIONAL LOGIC dual covers: on
Page 43 and 44: 38 EQUATIONAL LOGIC (Some prelimina
Page 45 and 46: 40 EQUATIONAL LOGIC semilattices (c
Page 47 and 48: 42 EQUATIONAL LOGIC a congruence on
Page 49 and 50: 44 EQUATIONAL LOGIC compactificatio
Page 51 and 52: 46 EQUATIONAL LOGIC precise definit
Page 53 and 54: 48 EQUATIONAL LOGIC 16. Connections
Page 55 and 56: 50 EQUATIONAL LOGIC 17.3. See e.g.
Page 58 and 59: REFERENCES This is not really a com
Page 60 and 61: 52.* __ , Current trends in algebra
Page 62 and 63: Universalis, 2(1972), 317-323. { 12
Page 64 and 65: Math. Bull., 18(1975), 427-429. 161
Page 66 and 67: 216. Jones, G. T., Pseudocomplement
Page 70 and 71: 324. The lattice of equational clas
Page 72 and 73: Soc., 23(1976), A-93. {16.7) 379. R
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Page 77 and 78: 72 , Certain algorithmic problems f
Page 79 and 80: 74 161-171. Fajtlowicz, S. and E. M
Page 81 and 82: 76 Goetz, A. and C. Ryll-Nardzewski
Page 83 and 84: 78 sets and general algebra, Acta.
Page 85 and 86: 8O Newman, M. H. A., A characteriza
Page 87 and 88: 82 __, Trellis theory, Memoirs Amer
Page 89: The Department of Mathematics and t
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