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Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction........................................................................................................................................................................................................................5
0. Terminology and preliminaries......................................................................................................................................................................................12
1. The extent of cut elimination by absorption..................................................................................................................................................................17
2. ∏¹-completeness of second order logic and a new proof of the normal form theorem.................................................................................................24
3. Weak models and proper three-valued models of second order theories....................................................................................................................31
4. Model theoretic proofs of the normal form theorem for higher order systems: comparison with the literature..............................................................39
5. Completeness of the systems $JT^n$ and $∏^n$-completeness of $∑^n$-theories.....................................................................................................43
6. ∀-analytical completeness of the systems $JPRE^n$ and poor completeness of the theories $PRE^n$ of primitive recursive equations....................48
7. ∀¹ ∃⁰-completeness of PRE² and König's Lemma for primitive recursive 0-1-trees......................................................................................................56
References.......................................................................................................................................................................................................................62
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
207
Liczba stron
62
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCVII
Daty
wydano
1983
Twórcy
autor
- Universität Hannover
Bibliografia
- [1] H. Friedman, Provable equality in primitive recursive arithmetic with and without induction, Pacific Journal Math. 57 (1975), 379-392.
- [2] G. Gentzen, Untersuchungen über das logische Schliessen. I., Math. Zeitschrift 39 (1935), 176-210.
- [3] J. Y. Girard, Three-valued logic and cut-elimination: The actual meaning of Takeuti's conjecture, Diss. Math. 136, Warszawa 1976.
- [4] R. L. Goodstein. Recursive number theory, Amsterdam 1957.
- [5] G. Kreisel and G. Takeuti, Formally self-referential propositions for cut free classical analysis and related systems, Diss. Math. 118, Warszawa 1974.
- [6] P. Päppinghaus, Existentiell schwache Vollständigkeit der Logik zweiter Stufe und Schnittelimination, Dissertation, Univ. Heidelberg, Heidelberg 1977.
- [7] D. Prawitz, Completeness and Hauptsatz for second order logic, Theoria 33 (1967), 246-253.
- [8] D. Prawitz, Hauptsatz for higher order logic, JSL 33 (1968), 452-457.
- [9] D. Prawitz, Some results for intuitionistic logic with second order quantification rules, in: A. Kino, J. Myhill, R. E. Vesley (eds.), Intuitionism and proof theory. Proc. of the summer conf. at Buffalo N. Y. 1968, Amsterdam 1970, 259-269.
- [10] K. Schütte, Syntactical and semantical properties of simple type theory, JSL 25 (1960), 305-326.
- [11] J. R. Shoenfield, Mathematical logic, Reading, Mass. 1967.
- [12] W. W. Tait, A non-constructive proof of Gentzen's Hauptsatz for second order predicate logic, Bull. AMS 72 (1966), 980-983.
- [13] M. Takahashi, A proof of cut-elimination theorem in simple type theory, J. Math. Soc. Japan 19 (1967), 399-410.
- [14] M. Takahashi, Review of [12], JSL 33 (1968), 289-290.
- [15] M. Takahashi, A system of simple type theory of Gentzen style with inference on extensionality, and the cut-elimination in it, Comment, math. Univ. Sancti Pauli 18 (1969), 129-147.
- [16] G. Takeuti, On a generalized logical calculus, Jap. J. Math. 23 (1953), 39-96.
- [17] G. Takeuti, Proof theory, Amsterdam 1975.
- [18] A. S. Troelstra, Metamathematical investigation of intuitionistic arithmetic and analysis, Berlin-Heidelberg-New York 1973.
- [19] H. Wolter, Über Mengen von Ausdrücken der Logik höherer Stufe, für die der Endlichkeitssatz und der Satz von Löwenheim-Skolem gelten, Zeitschr. f. math. Logik und Grundlagen d. Math. 18 (1972), 13-18.
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Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-ea62dbfc-3044-4b08-8dc8-3ed809a7fb93
Identyfikatory
ISBN
83-01-02639-1
ISSN
0012-3862
Kolekcja
DML-PL
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