Generalized Post algebras and their application to some infinitary many-valued logics

Nguyen, Cat-Ho

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Tytuł książki

Generalized Post algebras and their application to some infinitary many-valued logics

Autorzy

Cat-Ho Nguyen

Seria

Rozprawy Matematyczne tom/nr w serii: 107 wydano: 1973

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CONTENTS
Introduction............................................................................................................................................................................... 5
Part I. A generalization of Post algebras............................................................................................................................. 7
   1. Definition and characterization of generalized Post algebras............................................. 7
   2. Post subalgebras and Post homomorphisms...................................................................... 15
   3. Filters in the Post and semi-Post algebras. Quotient algebras......................................... 26
   4. Post algebras of type ν................................................................................................................ 35
   5. m-Representability of generalized Post algebras................................................................. 40
Part II. Infinitary propositional ν-valued languages........................................................................................................... 55
   1. A fundamental formal system $S(ℒ^ν_m)$............................................................................ 56
   2. Completeness of some formal systems based on languages $ℒ^ν_m$....................... 64
References............................................................................................................................................................................... 71

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Seria

Rozprawy Matematyczne tom/nr w serii: 107

Liczba stron

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CVII

Daty

wydano

1973

Twórcy

autor

Cat-Ho Nguyen

Bibliografia

[1] C. C. Chang, On representation of a-complete Boolean algebras, Trans. Amer. Math. Soc. 85 (1967), p. 208—218.
[2] C. C. Chang, Algebraic analysis of many-valued logic, ibidem 88 (1958), p. 467 —490.
[3] C. C. Chang, and A. Horn, Prime ideal characterization of generalised Post algebras, Proc. Symp. Pure Math. II (1961), p. 43—48.
[4] Ph. Dwinger, Notes on Post algebras I, II, Indag Math. 28 (1966), p. 462—478.
[5] Ph. Dwinger, Generalized Post algebras, Bull. Acad. Polon. Sci., Sér. sci. math, astronom. et phys. 16 (1968), p. 559.
[6] Ph. Dwinger, Ideals in generalized Post algebras, ibidem 17 (1969), p. 483—486.
[7] G. Epstein, The lattice theory of Post algebras, Trans. Amer. Math. Soc. 95 (1960), p. 300-317.
[8] L. Henkin, Boolean representation through propositional calculus, Fund. Math. 41 (1964), p. 89-96.
[9] L. Henkin, Fragments of the propositional calculus, J. Symbolic Logic 14 (1949), p. 42-48.
[10] L. Henkin, Some remarks on infinitely long formulas, Infinitistic Methods, Warszawa 1969, p. 167-183.
[11] C. Karp, Languages with Expression in Infinite Length, Studies in Logic and Foundations of Mathematics, Amsterdam (North-Holland), 1964.
[12] V. G. Kirin, Gentzen's method for the many-valued propositional calculi, Z. Math. Logik Grundlagen Math. 12 (1966), p. 317 — 332.
[13] V. G. Kirin, Post algebras as semantic bases of some many-valued logics, Fund. Math. 63 (1968), p. 279-294.
[14] S. C. Kleene, Introduction to metamathematics, Amsterdam — Groningen —New York 1952.
[15] S. Maehara and G. Takeuti, A formal system of first-order predicate calculus with infinitely long expressions, J. Math. Soc. Japan 13 (1961), p. 357—370.
[16] H. Rasiowa, Algebraic treatment of the functional calculi of Heyting and Lewis, Fund. Math. 38 (1951), p. 99-120.
[17] H. Rasiowa, A theorem on the existence of prime filters in Post algebras and the completeness theorem for some many-valued predicate calculi, Bull. Acad. Polon. Sci., Sér., sci. math, astronom. et phys. 17 (1969), p. 347—354.
[18] H. Rasiowa, Ultraproducts of m-valued models and a generalization of the Löwenheim—Skolem—Gödel—Malcew Theorem for theories based on m-valued logics, ibidem 18 (1970), p. 415-420.
[19] H. Rasiowa, and R. Sikorski, A proof of the completeness theorem of Gödel, Fund. Math. 37 (1950), p. 193-200.
[20] H. Rasiowa, A proof of Skolem—Löwenheim theorem, ibidem 38 (1951), p. 230—232.
[21] H. Rasiowa, The mathematics of metamathematics, Warszawa 1963.
[22] L. Rieger, On free $ℵ_ξ$-complete Boolean algebras, Fund. Math. 38 (1951), p. 35 —52.
[23] G. Rousseau, Logical systems with finitely many truth-values, Bull. Scad. Polon. Sci., Sér. sci. math, astronom. et phys. 17 (1969), p. 189—194.
[24] G. Rousseau, Post algebras and pseudo-Post algebras, Fund. Math. 67 (1970), p. 133—145.
[25] H. Sawicka, On some properties od Post algebras with countable chain of constants (to appear).
[26] D. Scott and A. Tarski, The sentential calculus with infinitely long Expressions, Colloq. Math. 6 (1958), p. 166—170.
[27] R. Sikorski, Boolean algebras, Berlin — Göttingen — Heidelberg 1960.
[28] A. Tarski, Remarks on predicate logic with infinitely long expressions, Colloq. Math. 6 (1958), p. 171—176.
[29] T. Traczyk, Axioms and some properties of Post algebras, ibidem 10 (1963), p. 193-209.
[30] T. Traczyk, Some theorems on independence in Post algebras, Bull. Acad. Polon. Sci., Sér. sci. math, astronom, et phys. 11 (1963), p. 3—8.
[31] T. Traczyk, 4 generalization of the Loomis-SihorsM theorem, Colloq. Math. 12 (1964), p. 155-161.
[32] T. Traczyk, On Post algebras with uncountable chain of constants. Algebras of Homo-morphisms, Bull. Acad. Polon. Sci., Sér., sci. math, astronom, et phys. 15 (1967), p. 673-680.
[33] T. Traczyk, Prime ideals in generalized Post algebras, ibidem 16 (1968), p. 369—373.
[34] E. Włodarska, On the representation of Post algebras preserving some infinite joins and meets, ibidem 18 (1970), p. 49—54.

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