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Pełne teksty:
Warianty tytułu
Abstrakty
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
autor
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.
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ISSN
0012-3862
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