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Rasiowa H. — An algebraic approach to non-classical logics (Studies in logic and the foundations of mathematics volume 78)
Rasiowa H. — An algebraic approach to non-classical logics (Studies in logic and the foundations of mathematics volume 78)

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Название: An algebraic approach to non-classical logics (Studies in logic and the foundations of mathematics volume 78)

Автор: Rasiowa H.

Аннотация:

The main aim of the present book is to formulate an algebraic approach to a carefully selected widest possible class of logics and to prove fundamental theorems for it, which previously have usually been proved for each of those logics separately.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 249

Добавлена в каталог: 23.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathscr N$-lattices      67
$\nu$-filter      262
${T}_{0}$-space      7
${\bf L}_{m}$, m-valued semantic      340
${\bf L}_{m}$-model      340
${\bf L}_{\chi}$, semantic      267
${\bf L}_{\chi}$-model      267
${\bf L}_{\lambda}$, I-semantic      323
${\bf L}_{\lambda}$-model      323
${\bf L}_{\mathscr N}$-model      295
${\bf L}_{\mu}$-model      256
${\bf L}_{\nu}$-model      261
${\bf L}_{\pi i}$-model      217
${\bf L}_{\pi}$-model      244
${\bf L}_{\varkappa i}$, semantic      227
${\bf L}_{\varkappa i}$-model      227
${\bf L}_{\varkappa}$, semantic      315
${\bf L}_{\varkappa}$-model      315
${\mathscr S}$-algebra      181
${\mathscr S}$-algebra, complete      363
${\mathscr S}$-valid formula      185
${\mathscr S}_{m}$-algebras      337
${\mathscr S}_{\chi}$-algebras      264
${\mathscr S}_{\lambda}$-algebras      319
${\mathscr S}_{\mathscr N}$-algebras      282
${\mathscr S}_{\mu}$-algebras      253
${\mathscr S}_{\nu}$-algebras      259
${\mathscr S}_{\pi i}$-algebras      213
${\mathscr S}_{\pi}$-algebras      237
${\mathscr S}_{\varkappa i}$-algebras      222
${\mathscr S}_{\varkappa}$-algebras      314
${\rm L}_{m}$-theories of zero order      340
${\rm L}_{m}$-theories of zero order, prime      344
${\rm L}_{m}$-valid      339
${\rm L}_{\chi}$-theories of zero order      267
${\rm L}_{\chi}$-theories of zero order, prime      271
${\rm L}_{\chi}$-valid      265
${\rm L}_{\lambda}$-theories of zero order      323
${\rm L}_{\lambda}$-theories of zero order, I-prime      328
${\rm L}_{\lambda}$-valid      320
${\rm L}_{\mathscr N}$-theories of zero order      295
${\rm L}_{\mathscr N}$-theories of zero order, prime      301
${\rm L}_{\mathscr N}$-valid      284
${\rm L}_{\mu}$-theories of zero order      255
${\rm L}_{\mu}$-valid      254
${\rm L}_{\nu}$-theories of zero order      261
${\rm L}_{\nu}$-valid      259
${\rm L}_{\pi i}$-theories of zero order      217
${\rm L}_{\pi i}$-valid      215
${\rm L}_{\pi}$-thcories, of zero, order      244
${\rm L}_{\pi}$-thcories, prime      247
${\rm L}_{\pi}$-valid      239
${\rm L}_{\varkappa i}$-theories of zero order      226
${\rm L}_{\varkappa i}$-valid      224
${\rm L}_{\varkappa}$-theories of zero order      315
${\rm L}_{\varkappa}$-valid      314
.m-argument operation      9
.m-element sequence      4
.m-valued logic ${\rm L}_{m}$      338
.m-valued logic ${\rm L}_{m}$, propositional calculus of      336
.m-valued semantic model      340
.von Bummert, J.      vii 167 390
Abbott, J.C.      vii 16 30 380
Abstract algebra      9
Ackerman, W.      315 383
Adequate L-model      190 375
Algebra      9
Algebra, associated with a formalized language of zero order      174
Algebra, degenerate      9
Algebra, free in a class K      11
Algebra, generalized      14
Algebra, generalized complete      14
Algebra, generalized free for a class K      14
Algebra, implicative      16
Algebra, of a propositional calculus      183
Algebra, of a theory      191 364
Algebra, of formulas      172 353
Algebra, of terms      358
Algebras, isomorphic      10
Algebras, similar      10
Alphabet of a formalized language      170 351
Antisymmetric relation      7
Auxiliary signs      171
Barcan, R.C.      311 380
Base of a topological space      6
Bergmann, G.      311 380
Bernays, P.      210 212 221 234 241 243 383
Beth, E.W.      ix 250 311 380
Bialynicki — Birula      38 44 45 47 49 50 67 82 90 104 106 276 277 278 284 286 288 289 291 293 295 309 310 350 378 379 380
Binary propositional connectives      170 351
Birkhoff, G.      39 44 51 380
Boole, G.      v 167
Boolean algebra      111
Boolean algebra, topological      115
Bound individual variables      352
Brignole, D.      67 75 107 380
Brouwer, L.E.J.      250 381
Brouwerian algebra      52
Canonical realization for elementary L-theory      370
Canonical realization of terms      361
Canonical valuation      177 361
Carnap, R.      311 381
Cartesian product      4
Cech, E.      130 381
Chain      8
Chain, of deductive niters      202
Chain, of implicative filters      18
Chandrasekharan, K.      250 251 366 381
Chang, C.C.      132 381
Characteristic valuation for ${\bf L}_{\chi}$-theories      272
Characteristic valuation for ${\bf L}_{\lambda}$-theories      329
Characteristic valuation for ${\bf L}_{\mathcal N}$-theories      305
Chateaubriand, O.      49 381
Church, A.      212 381
Classical implicative logic      223
Classical implicative logic, propositional calculus of      221
Classical logic      314
Classical logic, propositional calculus of      314
Classical theory of zero order      315
Closed element in a topological Boolean algebra      116
Closed set      5
Closure algebras      110
Closure, of a set      5
Closure, of an element      115
Closure, operation      5 116
Compact space      6
Compact, strongly      121
Complement      3 112
Complement, contrapositional      58
Complementation      111
Complemented element      112
Complete generalized algebra      14
Complete implicative algebra      362
Completeness theorem for first order predicate calculi of a logic L      374
Completeness theorem for propositional calculi in S      185
Completeness theorem for propositional calculi of a logic L      186
Completeness theorem for propositional calculi of classical implicative logic      224
Completeness theorem for propositional calculi of classical logic      315
Completeness theorem for propositional calculi of constructive logic with strong negation      284
Completeness theorem for propositional calculi of intuitionistic logic      265
Completeness theorem for propositional calculi of m-valued logic      340
Completeness theorem for propositional calculi of minimal logic      254
Completeness theorem for propositional calculi of modal logic      320
Completeness theorem for propositional calculi of positive implicative logic      215
Completeness theorem for propositional calculi of positive logic      239
Completeness theorem for propositional calculi of positive logic with semi-negation      260
Composition of mappings      4
Conclusion      178
Congruence relation      11
Conjunction sign      235
Connective, propositional      170
Consequence operation      177 178 355
Consistent elementary L-theory      358
Consistent L-theory of zero order      189
Consistent propositional calculus      180
Constructible falsity, property of      302
Constructible falsity, theorem on      293
Constructive logic with strong negation      283
Constructive logic with strong propositional, calculus of      279
Contraposition law      58
Contrapositional complement      58
Contrapositional negation sign      252
Contrapositionally complemented implication algebra      37
Contrapositionally complemented lattice      58
Contrapositionally complemented positive implication algebra      36
D-filter      144
D-filter, irreducible      144
D-filter, maxima!      144
D-filter, prime      144
D-filter, principal      144
D-filter, proper      144
De Morgan lattice      44
Deduction theorems      219 229 246 258 270 299 326 327 343 344
Deductive filter      200
Deductive filter, generated by a set      202
Deductive filter, irreducible      202
Deductive filter, maximal      203
Deductive filter, proper      202
Deductive filters, chain of      202
Degenerate algebra      9
Dense element      125
Dense set      6
Derivable formula in a predicate calculus      356
Derivable, formulas in a propositional calculus, set of      179
Diego, A.      vii 16 25 26 28 381
Direct subformula      171
Disjunction sign      235
Distributive lattice      43
Distributive laws      43
Domain      4
Dugundji, J.      320 381
Dummet, M.      275 332 381
Dwinger, P.      132 156 160 161 381
Dyson, V.H.      250 382
Element, closed      116
Element, complemented      112
Element, dense      125
Element, open      116
Element, prime      108
Elementary L-theory      357
Elementary L-theory, consistent      358
Elementary L-theory, irreducible      358
Elementary L-theory, maximal      358
Elementary L-theory, the algebra of      364
Empty set      3
Epimorphism      10
Epstein, G.      132 164 382
Existential quantifier sign      352
Extension of a formalized language of zero order      171
Field of sets      111
Field of sets, generated by a set      42
Field of sets, irreducible      42
Field of sets, maximal      42
Field of sets, prime      42
Field of sets, principal      41
Field of sets, proper      42
Field of sets, topological      115
Field of sets, unit      41
Filter      41
Finite, character of a consequence operation      177
First order formalized language associated with a logic L      353
First order predicate calculus of a logic L      355
Formal proof      178 180 189 355
Formalized language of zero order      171
Formula      171 352
Formula, ${\mathscr S}$-valid      185
Formula, atomic      353
Formula, derivable in ${\mathscr S}$      179
Formula, derivable in ${\mathscr S}^{*}$      356
Formula, L-valid      186 371
Formula, satisfiable in R      371
Formula, valid in 21      185
Formula, valid in a realization R      371
Free algebra in a class K      11
Free generalized algebra      14
Free generators, set of      11 14
Free individual variables      352
Functionally complete Post algebra      142
Functionally complete propositional calculus of m-valued logic      334
Functionally free quasi-Boolean algebra      49
functors      352
Gastaminza, S.      49 382
Gastaminza.M.L.      49 382
Generalized algebra      14
Generalized algebra, free for a class K      14
Generalized join      362
Generalized join, preserved by a homomorphism      363
Generalized meet      362
Generalized meet preserved by a homorphism      363
Generalized meets corresponding to quantifiers      366
Generalized, joins corresponding to quantifiers      366
Generators of a deductive filter, set of      202
Generators, set of      10
Gentzen, G.      250 266 267 334 382
Glivenko, V.      250 274 382
Godel, K.      V 250 267 274 377 382
Greatest element      8
Greatest lower bound      8
Guillaume, M.      311 382
Hallden, S.      383
Halmos, P.R.      vi 382
Hanf, W.      vi 382
Hausdorff space      7
Henkin, L.      v vi 16 22 44 210 212 215 250 251 331 348 349 366 368 370 375 383
Herbrand, J.      317 383
Heyting algebra      52
Heyting, A.      ix 250 263 383
Hilbert algebras      16
Hilbert, D.      210 212 234 241 243 315 383
Hintikka, J.      311 383
Homeomorphic, topological spaces      7
Homomorphism      10
Homomorphism preserving a congruence      12
Homomorphism preserving a generalized join      (meet) 363
Horn, A.      132 210 233 242 248 249 275 381 383
Hosoi, T.      250 384
I-filter      116
I-filter, generated by a set      117
I-filter, I-prime      117
I-filter, irreducible      117
I-filter, maximal      117
I-filter, principal      117
I-filter, proper      117
I-filter, unit      116
I-prime ${\bf L}_{\lambda}$-theory of zero order      328
I-prime I-filter      117
I-semantic model      323
Ideal      41
Ideal, generated by a set      42
Ideal, irreducible      42
Ideal, maximal      42
Ideal, prime      42
Ideal, principal      41
Ideal, proper      42
Ideal, zero      41
Idividual constants      352
Idividual variables      352
Idividual variables, bound      352
Idividual variables, free      352
Image      4
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