Definable quantifiers in second order arithmetic and elementary extensions of ω-models

Guzicki, Wojciech

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Tytuł książki

Definable quantifiers in second order arithmetic and elementary extensions of ω-models

Autorzy

Wojciech Guzicki

Seria

Rozprawy Matematyczne tom/nr w serii: 208 wydano: 1983

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Abstrakty

CONTENTS
0. Introduction and terminology..............................................................5
1. Quantifiers and elementary extensions..............................................8
2. Elementary extensions of countable models of set theory................15
3. Interpretations of set theory in extensions of A₂...............................21
4. Definable quantifiers in models of A₂...............................................32
5. Elementary generic extensions........................................................40
References..........................................................................................50

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Seria

Rozprawy Matematyczne tom/nr w serii: 208

Liczba stron

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCVIII

Daty

wydano

1983

Twórcy

autor

Wojciech Guzicki

Bibliografia

[1] K. Apt and W. Marek, Second order arithmetic and related topics, Ann. Math. Logic 6 (1974), pp. 177-229.
[2] F. Drake, Set theory, North Holland, Amsterdam 1974.
[3] M. Dubiel, Generalized quantifiers and elementary extensions of countable models, J. Symb. Logic 42 (1977), pp. 341-348.
[4] M. Dubiel, Generalized quantifiers in models of set theory, Fund. Math. 106, 1980, pp. 153-161.
[5] W. Guzicki, Uncountable β-models with countable height, Fund. Math. 82 (1974), pp. 143-152.
[6] W. Guzicki, Elementary extensions of Levy's model of A₂̄ , Synthese 27 (1974), pp. 265-270.
[7] W. Guzicki, Interpretations of set theories in extensions of A₂, abstract, J. Symb. Logic 41 (1976), p. 266.
[8] W. Guzicki, On the projective class of the continuum hypothesis, Set theory and the Hierarchy Theory V, Springer Verlag 1977, pp. 181-186.
[9] W. Guzicki, The equivalence of definable quantifiers in second order arithmetic, Fund. Math. 113 (1981), pp. 59-65.
[10] L. Harrington, Long projective wellorderings, Ann. Math. Logic 12 (1977), pp. 1-24.
[11] T. E. Hutchinson, Elementary extension of countable models of set theory, J. Symb. Logic 41 (1976), pp. 139-145.
[12] T. J. Jech, Lectures in Set Theory. Springer Verlag, 1971.
[13] H. J. Keisler, Logic with the quantifier "there exist uncountably many", Ann. Math. Logic I (1970), pp. 1-93.
[14] H. J. Keisler, Model theory of infinitary logic. North Holland, Amsterdam 1971.
[15] H. J. Keisler and M. Morley, Elementary extensions of models of set theory, Israel J. Math. 6 (1968), pp. 49-65.
[16] G. Kreisel, Survey of the proof theory I, J. Symb. Logic 33 (1968), pp. 321-388.
[17] J. L. Krivine and K. McAloon, Forcing and generalized quantifiers, Ann. Math. Logic 5 (1973), pp. 199-255.
[18] W. Marek, On the metamathematics of the impredicate set theory, Dissertationes Math. 98 (1973).
[19] W. Marek, Observations concerning elementary extensions of ω-models II, J. Symb. Logic 38 (1973), pp. 227-231.
[20] D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), pp. 143-178.
[21] A. Mostowski, On a generalization of quantifiers. Fund. Math. 44 (1957), pp. 12-36.
[22] A. Mostowski, Formal system of analysis based on an infinitary rule of proof, Infinitistic Methods, Warszawa-London 1960, pp. 141-166.
[23] A. Mostowski, A transfinite sequence of ω-models, J. Symb. Logic 37 (1972), pp. 96-102.
[24] A. Mostowski, Patrial orderings of the family of ω-models, Logic, Methodology and Philosophy of Science IV, North Holland. Amsterdam 1973, pp. 13-28.
[25] A. Mostowski, Observations concerning elementary extensions of ω-models I, Proceedings of AMS Symposia in Pure Mathematics 25 (1975), pp. 349-355.
[26] A. Mostowski and Y. Suzuki, On ω-models which are not β-models, Fund. Malh. 65 (1969), pp. 83-93.
[27] R. Platek, Eliminating the continuum hypothesis, J. Symb. Logic 34 (1969), pp. 219-225.
[28] R. M. Solovay, A model of set theory in which every set of reals is Lebesque measurable, Ann. Math. 92 (1970), pp. 1-57.
[29] R. M. Solovay and S. Tennenbaum, Iterated Cohen extensions and Suslin problem, Ann. Math. 94 (1970), pp. 201-245.
[30] A. Tarski, Pojęcie prawdy w językach nauk dedukcyjnych, Prace Towarzystwa Naukowego Warszawskiego, Nr 34, Warszawa 1933.
[31] J. Truss, Models of set theory containing many perfect sets, Ann. Math. Logic 7 (1974), pp. 197-219.
[32] A. Zarach, Forcing with proper classes, Fund. Math. 81 (1973), pp. 1-27.
[33] P. Zbierski, Models for higher order-arithmetics, Bull. Acad. Polon, Sci. 19 (1971), pp. 557-562.

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Identyfikator YADDA

bwmeta1.element.zamlynska-24c8cb4f-f784-4521-bb44-f288866f8681

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ISBN

83-01-02720-7

ISSN

0012-3862

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DML-PL

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