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Propositional extensions of $L_ω_1_ω$

Seria
Rozprawy Matematyczne tom/nr w serii: 169 wydano: 1980
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Warianty tytułu
Abstrakty
EN
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
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
Bibliografia
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  • [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.
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  • [13] H. Friedman, Adding propositional connectives to countable infinitary logic, to appear.
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  • [15] R. Gostanian, The next admissible ordinal, Annals of Math. Logic 17 (1979).
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  • [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.
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  • [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).
Języki publikacji
EN
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-027e2ec7-282a-4661-a459-0635e6cb59d0
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ISBN
83-01-01105-X
ISSN
0012-3862
Kolekcja
DML-PL
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