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An algebraic and Kripke-style approach to a certain extension of intuitionistic logic

Seria
Rozprawy Matematyczne tom/nr w serii: 167 wydano: 1980
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Abstrakty
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CONTENTS

Introduction............................................................................... 5

Chapter I. Semi-Boolean algebras

 1. Semi-Boolean algebras....................................... 8
 2. Q-filters in semi-Boolean algebras............................ 11
 3. Extensions of semi-Boolean algebras...................... 15

Chapter II. Algebraic and semantic models
for Heyting-Brouwer logic

 1. Preliminaries.......................................................... 17
 2. Algebraic structures....................................................... 21
 3. Completeness theorems............................................. 23
 4. Deduction theorems...................................................... 24
 5. Saturated H-B theories................................................. 26
 6. Craig interpolation lemma........................................... 29
 7. Theory of falsity............................................................... 31
 8. Kripke-style models....................................................... 34
 9. Canonical structures..................................................... 39
 10. Connections between a-models and k-models.... 42

Chapter III. Model theory for Heyting-Brouwer logic

 1. Ultraproducts.......................................................... 45
 2. Model extension theorem............................................. 47
 3. Connections between H-B logic and DI logic........... 56
References....................................................................................... 59
List of symbols................................................................................. 60
List of definitions............................................................................. 61
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 167
Liczba stron
62
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CLXVII
Daty
wydano
1980
Twórcy
Bibliografia
  • [1] E. W. Beth, Semantic entailment and formal derivability, Meded. d. Koninkl. Nederl. Acad, van Wetensch Afd. Letterk 18 (1955).
  • [2] K. A. Bowen, Normal Model Theory, Journal of Philosophical Logic, 4 (1975), pp. 97-131.
  • [3] V. H. Dyson and G. Kreisel, Analysis of Beth's construction of intuitionistic logic, mimeographed 1961.
  • [4] M. C. Fitting, Intuitionistic Logic, Model Theory and Forcing, North-Holland, Amsterdam-London 1969.
  • [5] M. C. Fitting, Model Existence Theorem for modal and intuitionistic logic, J. S. L. 38 (1973), pp. 613-627.
  • [6] D. M. Gabbay, Applications of trees to intermediate logics, J. 3. L. 37 (1973), pp. 135-139.
  • [7] D. M. Gabbay, Model Theory for Intuitionistic Logic, Zeitschr. f. math. Logic und Grundlagen d. Math. 18 (1972), pp. 49-54.
  • [8] S. Görnemann, Logic stronger than intuitionism, J. S. L. 36 (1971), pp. 249-261.
  • [9] A. Grzegorczyk, A philosophically plausible formal interpretation of intuitionistic logic, Indag. Math. 26 (1964), pp. 596-601.
  • [10] A. Grzegorczyk, Some relational systems and the associated topological spaces. Fund. Math. 60 (1967), pp. 223-231.
  • [11] D. H. J. de Jongh, Recherches sur les I-valuations, Rapp. Euraton, CETN, 1962.
  • [12] S. A. Kripke, Semantical analysis of intuitionistic logic I, in: J. N. Crossley and M. A. Dummet (Eds.), Formal systems and recursive functions, North-Holland, Amsterdam 1965.
  • [13] J. C. C. Mc Kinsey and A. Tarski, On Closed Elements in Closure Algebras, Ann. of Math. 47 (1946), pp. 122-162.
  • [14] A. Mostowski, Proofs of non-deducibility in intuitionistic functional calculus, J. S. L. 13 (1948), pp. 204-207.
  • [15] H. Rasiowa and R. Sikorski, The Mathematics of the Metamathematics, PWN, Warsaw 1963.
  • [16] C. Rauszer, Semi-Boolean algebras and their applications to intuitionistic logic with dual operations, Fund. Math. 83 (1974), pp. 219-249.
  • [17] C. Rauszer, On the Strong Semantical Completeness of Any Extension of the Intuitionistic Predicate Calculus, Bull. Acad. Polon. Sci. 2 (1976), pp. 81-87.
  • [18] C. Rauszer and B. Sabalski, Remarks on Distributive Pseudo-Boolean algebras. Bull. Acad. Polon. Sci. 2 (1975), pp. 123-129.
  • [19] C. Rauszer, Model theory for an extension of intuitionistic logic, Studia Logica 36 (1-2) (1977), pp. 73-87.
  • [20] J. R. Shoenfield, Mathematical Logic, Addison-Wesley 1967.
  • [21] R. H. Thomason, On the Strong Semantical Completeness of the Intuitionistic Predicate Calculus, J. S. L. 33 (1968), pp. 1-7.
  • [22] D. Vakarelov, Representation theorems for semi-Boolean algebras and semantics for Heyting-Brouwer logic, Bull. Acad. Polon. Sci. 11 (1974), pp. 1087-1095.
Języki publikacji
EN
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-3b6ab1b7-eb0b-46ec-bf99-c72703fc57d7
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ISBN
83-01-01103-3
ISSN
0012-3862
Kolekcja
DML-PL
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