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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
0. Preliminaries....................................................................... 7
1. Adding propositional connectives to $L_ω_1_ω$............... 8
2. The propositional part of $L_ω_1_ω$ (S)............................. 10
3. The operation S and the Boolean algebra $B_S$............... 11
4. General model-theoretic properties of $L_ω_1_ω$(S)...... 17
5. Hanf number computations...................................................... 22
6. Negative results for $L_ω_1_ω$(S)........................................ 27
7. Proposition al extensions of $L_ω_1_ω$
a in the constructible universe...................................................... 34
8. The Souslin connective.............................................................. 44
9. Concluding remarks................................................................... 49
References....................................................................................... 53
0. Preliminaries....................................................................... 7
1. Adding propositional connectives to $L_ω_1_ω$............... 8
2. The propositional part of $L_ω_1_ω$ (S)............................. 10
3. The operation S and the Boolean algebra $B_S$............... 11
4. General model-theoretic properties of $L_ω_1_ω$(S)...... 17
5. Hanf number computations...................................................... 22
6. Negative results for $L_ω_1_ω$(S)........................................ 27
7. Proposition al extensions of $L_ω_1_ω$
a in the constructible universe...................................................... 34
8. The Souslin connective.............................................................. 44
9. Concluding remarks................................................................... 49
References....................................................................................... 53
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
169
Liczba stron
54
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CLXIX
Daty
wydano
1980
Twórcy
autor
autor
Bibliografia
- [1] P. Aczél and W. Richter, Inductive definitions and analogues of large cardinals, in: Generalized recursion theory, North Holland, Amsterdam 1973.
- [2] J. Barwise, Infinitary logins and admissible sets, J. Symbolic Logic 34 (1965), pp. 220-252.
- [3] J. Barwise, Absolute logics and $L_{∞ω}$ Ann. Math. Logic 4 (1972), pp. 309-340.
- [4] J. Barwise and K. Kunen, Hanf numbers for fragments of $L_{∞ω}$, Israel J. Math. 10 (1971), pp. 306-320.
- [5] J. Barwise, E. Gandy and Y. N. Moschovakis, The next admissible set, J. Symbolic Logic 36 (1971), pp. 108-120.
- [6] D. Busch, On the number of Solovay r-degrees, Zeitschrift fur Math. Logik und Grundlagen der Mathematik 22 (1976), pp. 283-286.
- [7] P. Campbell, Souslin logic (abstract), Notices Amer. Math. Soc. 19 (1972), p. A-599.
- [8] K. Devlin, Aspects of constructibility, Springer 1974.
- [9] M. A. Dickmann, Large infinitary languages, North Holland, Amsterdam 1975.
- [10] E. Ellentuck, The foundations of Souslin logic, J. Symbolic Logic 40 (1975), pp. 567-575.
- [11] S. Feferman, Lectures on proof theory, in: Proc. of the Summer School in Logic, Leeds 1967, Springer 1968.
- [12] H. Friedman, Determinacy in the low projective hierarchy, Fund. Math. 72 (1971), pp. 79-95.
- [13] H. Friedman, Adding propositional connectives to countable infinitary logic, to appear.
- [14] R. O. Gandy, Proof of Mostowski's conjecture, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 8 (1960), pp. 571-575.
- [15] R. Gostanian, The next admissible ordinal, Annals of Math. Logic 17 (1979).
- [16] R. Gostanian and K. Hrbacek, On the failure of the weak Beth property, Proc. Amer. Math. Soc. 58 (1976), pp. 245-249.
- [17] F. Halpern, Some Barwise type results for Souslin logic, preprint.
- [18] C. Karp, Languages with expressions of infinite length, North Holland, Amsterdam 1964.
- [19] H. J. Keisler, Model theory for infinitary logic, North Holland, Amsterdam 1971.
- [20] S. C. Kleene, On the forms of the predicates in the theory of constructive ordinals, (second paper) Amer. J. Math. 77 (1956), pp. 405-428.
- [21] G. Kreisel, Choice of infinitary languages by means of definability criteria, in: The Syntax and Semantics of Infinitary Languages, Springer 1968, pp. 135-151.
- [22] K. Kunen, Implicit definability and infinitary languages, J. Symbolic Logic 33 (1968), pp. 446-451.
- [23] P. Lindstrom, First order logic with generalized quantifiers, Theoria 32 (1966), pp. 186-195.
- [24] On extensions of elementary logic, Theoria 35 (1969), pp. 1-11.
- [25] D. A. Martin, Projective sets and cardinal numbers: some questions related to the continuum problem, to appear.
- [26] D. A. Martin, The Wadge ordering is a well-ordering, unpublished handwritten note.
- [27] A. Mostowski, An undecidable arithmetic statement, Fund. Math. 36 (1949), pp. 143-164.
- [28] J. Myhill and D. Scott, Ordinal definability, in: Axiomatic set theory (part I), Amer. Math. Society, Providence 1971.
- [29] D. Scott, Logic with denumerably long formulas and finite strings of quantities, in: The Proceedings of the Berkeley Symposium on the Theory of Models, Amsterdam 1965.
- [30] J. R. Shoenfield, Mathematical logic, Addison Wesley 1967.
- [31] R. Solovay, Determinacy and type-2 recursion (abstract), J. Symbolic Logic 36 (1971), p. 374.
- [32] R. Vaught, Descriptive set theory in $L_{ω_1ω}$, in: The Cambridge Summer School in Mathematical Logic, Springer 1974.
- [33] R. Vaught, Invariant sets in topology and logic, Fund. Math. 82 (1974), pp. 269-293.
- [34] W. Wadge, Degrees of complexity of subsets of the Baire space (abstract), Notices Amer Math. Soc. 19 (1972), p. A-714.
- [35] K. Hrbacek, On the complexity of analytic sets, Zeitschrift für Math. Logik und Grundlagen der Math. 24 (1978), pp. 419-425.
- [36] K. Hrbacek and S. Simpson, On Kleene degrees of analytic sets, in: The Proceedings of the Kleene Symposium, Madison, Wis., 1978, to appear.
- [37] R. Gostanian and K. Hrbacek, Propositional extensions of $L_{ω_1ω}$, I, II (abstracts), J. Symbolic Logic 42 (1977), pp. 125-126.
- [38] L. Harrington, Analytic determinacy and 0#, J. Symbolic Logic 43 (1978), pp. 685-693.
- [39] L. Harrington, Extensions of $L_{ω_1ω}$ which preserve most of its nice properties, Zeitschrift für Math. Logik und Grundlagen der Math, (to appear).
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bwmeta1.element.zamlynska-027e2ec7-282a-4661-a459-0635e6cb59d0
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83-01-01105-X
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0012-3862
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