Keywords
- Symbolic Logic
- Axiomatic Theory
- Absolute Property
- Craig Interpolation
- Undecidable Theory
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Bibliography of Mostowskt’s works
Abzahlbare Boole’sche Körper und ihre Anwendungen auf die allgemeine Metamathematik, Fundamenta Mathematicae XXIX (1937) pp 34–53.
O niezależności definicji skończoności w, systemie logiki. Appendix to Roczniki Polskiego Towarzystwa Matematycznego, volume XI (1938) pp 1–54.
Über gewisse universelle Relationen. Ann. Soc. Pol. de Math. XVII (1939) pp 117–118.
Über den Begriff der endlichen Menge. Sprawozdania Towarzystwa Naukowego Warszawskiego XXXI (1938) pp 13–20.
(+ A. Lindenbaum) Über Unabhägigkeit des Auswahlaxioms und einiger seiner Folgerungen. Sprawozdania Towarzystwa Naukowego Warszawskiego XXXI (1939) pp 27–32.
(+ A. Tarski) Boole’sche Ringe mit geordneter Basis. Fundamenta Mathematicae XXXII (1939) pp 69–86.
Über die Unabhängigkeit des Wohlordnungastzes von Ordnungsprinzip. Fundamenta Mathematicae XXXII (1939) pp 201–252.
Bemerkungen zum Begriff der inhaltlichen Widerspruchsfreiheit. Journal of Symbolic Logic 4 (1939) pp 113–114.
Remarque sur une note de W. Sierpiński. Fundamenta Mathematicae XXXIII (1946) pp 7–8.
Axiom of choice for finite sets. Fundamenta Mathematicae XXXIII (1945) pp 137–168.
O zdaniach nierozstrzygalnych w sformalizowanych systemach matematyki. Kwartalnik Filozoficzny XVI (1946) pp 223–276.
Mostowski Zarys teorii Galois. Appendix to course book “Algebra Wyzsza” by W. Sierpiński (1946) pp 371–428.
On definable sets of positive integers. Fundamenta Mathematicae XXXIV (1947) pp 81–112.
On absolute, properties of relations. Journal of Symbolic Logic 12 (1947) pp 33–42.
On the principle of dependent choices. Fundamenta Mathematicae XXXV (1948) pp 127–130.
Proofs of non-deducibility in intuitionistic functional calculus. Journal of Symbolic Logic 13 (1948) pp 193–203.
On a set of integers not definable by means of one quantifier predicates. Ann. Soc. Pol. de Math. XXI (1948) pp 114–119.
Logika Matematyczna. Monografie Matematyczne t.XVIII (1948) Warszawa-Wrocław pp XIII+338.
Un theoreme sur les nombres cos 2kπ/n. Colloquium Mathematicum I (1948) pp 195–196.
Mostowski Sur l’interpretation geometrique et topologique des notions logiques. Actes du X-eme Congres International de Philosophie(Amsterdam 11–18 Aout 1948) Amsterdam 1949 pp 610–617.
An undecidable arithmetical statement. Fundamenta Mathematicae XXXVI (1949) pp 143–164.
(+ A. Tarski) Arithmetical classes and types of well-ordered systems. Bull. Amer. Math. Soc. 55 (1949) p 65 (1992).
(+ A. Tarski) Undecidability on the arithmetic of integers and in the theory of rings. Journal of Symbolic Logic 14 (1949) p 76.
La vie et l’oeuvre de S. Dickstein. Prace Matematyczno-Fizyczne 47 (1949) pp 7–12.
Kilka refleksji na temat zadań logicznych z “matematyki”. Matematyka 3 (1950) pp 6–11.
On the rules of proof in the pure functional calculus of the first order. Journal of Symbolic Logic 16 (1951) pp 107–111.
Some impredicative definitions in the axiomatic set theory. Fundamenta Mathematicae XXXVII (1951) pp 111–124. Correction: ibid Some impredicative definitions in the axiomatic set theory. Fundamenta Mathematicae XXXVIII (1952) p 238.
A classification of logical systems. Studia Philosophica 4 (1951) pp 237–274.
(+ K. Kuratowski) Sur un probleme de la theorie des groupes et son rapport a la topologie. Colloquium Mathematicum II (1951) pp 212–215.
Groups connected with Boolean algebras. Colloquium Mathematicum II (1951) pp 216–219.
On direct product of theories. Journal of Symobolic Logic 17 (1952) pp 1–31.
On models of axiomatic systems. Fundamenta Mathematicae XXXIX (1952) pp 133–158.
(+ K. Kuratowski) Teoria Mnogości. Monografie Matematyczne XXVII Warszawa-Wrocław 1952 pp IX+311.
Mostowski Sentences undecidable in formalized arithmetic. in: Studies in Logic and the Foundations of Mathematics Amsterdam (1952) pp VIII+117.
A lemma concerning recursive functions and its applications. Bull. Acad. Pol. Sci. I (1953) pp 277–280 (wersja rosyjska pp 275–279).
On a system of axioms which has no recursively enumerable arithmetic model. Fundamenta Mathematicae XL (1953) pp 56–61.
O tzw. konstruktywnych prawach w matematyce. Myśl Filozoficzna 1 (7) (1953) pp 230–241.
(+ M. Stark) Algebra Wyzsza, cz. I. w serii: Biblioteka Matematyczna I 3 Warszawa 1953 pp VI+308.
(+ H. Rasiowa) O geometryczne j interpretacji wyrazeń logicznych. Studia Logica I (1952) pp 274–275.
Mostowski (+A. Tarski i R. M. Robinson) Undecidable theories. in: Studies in Logic and the Foundations of Mathematics Amsterdam 1953 pp IX+98.
(+ M. Stark) Algebra Wyzsza, cz.II. w serii: Biblioteka Matematyczna III Warszawa 1954 pp VII+173.
(+ M. Stark) Algebra Wyzsza, cz.III. w serii: Biblioteka Matematyczna IV Warszawa 1954 pp VII+262.
Współczesny stan badań nad podstawami matematyki. Prace Matematyczne 1 (1954) pp 13–55.
Sovremenno je sostajanie issledovanij po osnovani jam matematiki. Uspechi Mat. Nauk 9 (1954) pp 1–38.
Podstawy matematyki na VIII zjeździe matematyków polskich. Myśl Filozoficzna 2 (1954) pp 328–330.
Development and applications of the “projective” classification of sets of integers. Proceedings of the International Congress of Mathematicians Amsterdam 1954 vol. 1 pp 280–288.
(+ other logicians) The present state of investigations of foundations of mathematics. Rozprawy Matematyczne (Dissertationes Mathematicae) IX (1955) pp 1–48 (German translation: Die Hauptreferate des 8 polonisches Mathematiker Kongres, Berlin 1954 pp 11–44).
At formula without recursively enumerable model. Fundamenta Mathematicae XLII (1955) pp 125–140.
Examples of sets definable by means of two and three quantifiers. Fundamenta Mathematicae XLII (1955) pp 259–270.
Contributions to the theory of definable sets of integers and functions. Fundamenta Mathematicae XLII (1955) pp 271–275.
Mostowski (+ J. Łoś, H. Rasiowa) A proof of Herbrand’s theorem. Journal des Mathematiques Pures et Appliquees (1955) pp 19–54.
Eine verallgemeinerung eines Satzes von M. Deuring. Acta Scientiarum Math. Szeged XVI (1955) pp 197–201.
Wyznaczanie stopni niektórych liczb algebraicznych. Prace Matematyczne 1 (1955) pp 239–252.
Mostowski (+M. Stark) Elementy Algebry Wyższej. w serii: Biblioteka Matematyczna 16 I wyd. Warszawa 1955 (i dalsze wydania).
(+ A. Ehrenfeucht) Models of axiomatic theories admitting automorphisms. Fundamenta Mathematicae XLIII (1956) pp. 50–68.
Concerning a problem of H. Scholz. Zeitschrift für Mathematische Logik und Grundlagenforschung 2 (1956) pp 210–214.
On models of axiomatic set theory. Bull. Acad. Pol. Sci. (C1 III) IV (1956) pp. 663–668.
Mostowski Zamecanija k dokazatelstvam suscestvovanija standartnych modelej. Trudy 3-go Vsesojuznogo Matematiceskogo Zjazda 1956 Tom 4 Moskva AN SSSR 1959 pp 232–236.
Logika matematyczna na międzynarodowym zjeździe matematyków w Amsterdamie. Studia Logica IV (1956) pp 245–253.
L’oeuvre de J. Łukasiewicz dans le domaine de la logique mathematique. Fundamenta Mathematicae XLIV (1957) pp 1–11.
On a generalization of quantifiers. Fundamenta Mathematicae XLIV (1957) pp 12–36.
Computable sequences. Fundamenta Mathematicae XLIV (1957) pp 37–51.
On recursive models of formalized arithmetic. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. V (1957) pp 706–718.
(+ A. Grzegorczyk, Cz. Ryll-Nardzewski) The classical and ω-complete arithmetic. Journal of Symbolic Logic 23 (1958) pp 188–206.
On a problem of W. Kinna and K. Wagner. Colloquium Mathematicum VI (1958) pp 207–208.
Mostowski Quelques observations sur l’usage des methodes infinitistes dans la meta-mathematiques. 70 Colloquium du CNRS, Paris 1958.
(+ Cz. Ryll-Nardzewski) Representability of sets in models of axiomatic theories. Journal of Symbolic Logic 23 (1958) p 458.
Mostowski (+ M. Stark) Algebra Liniowa. w serii: Biblioteka Matematyczna 19 I wyd. Warszawa 1958 (i dalsze wydania).
Mostowski On various degrees of constructivism. in: Constructivity in Mathematics, Studies in Logic and foundations of mathematics Amsterdam 1959 pp. 178–194.
A class of models of second-order arithmetic. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. VII (1959) pp 401–404.
Mostowski Formal system of analysis based on an infinitary rule of proof. Proceedings of Warsaw Symposium on Infinitistic Methods. Warszawa-London 1960 pp 141–166.
A generalization of the incompleteness theorem. Fundamenta Mathematicae XLIV (1961) pp 205–232.
An example of a non-axiomatizable many-valued logic. Zeitschrift für Mathematische Logik und Grundlagenforschung 7 (1961) pp 72–76.
Mostowski Concerning the problem of axiomatizability of the field of real numbers in the weak second order logic. Essays in Fundations of Mathematics, Jerusalem 1961 pp 269–286.
(+ A. Grzegorczyk, Cz. Ryll-Nardzewski) Definability of sets in models of axiomatic theories. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. IX (1961) pp 163–167.
(+ A. Ehrenfeucht) A compact space of models for 1st order theories. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. IX (1961) pp 369–373.
Mostowski (+ J. Łoś, H. Rasiowa) Addition au travail “A proof of Herbrand theorem”. Journal des Mathematiques Pures et Appliques 1961 pp 129–134.
Mostowski Organizacja i prace naukowe Instytutu Matematyki Uniwersytetu Warszawskiego. Księga pamiątkowa dla uczczenia 140-lecia Uniwersytetu Warszawskiego. (1961).
Axiomatizability of some many-valued predicate calculi. Fundamenta Mathematicae L (1961–1962) pp 165–190.
Mostowski Representability of sets in formal systems. Proceedings of Symposium on Recursive Functions New York 1961 (1962) pp 29–48.
A problem in the theory of models. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. X (1962) pp 121–126.
On invariant, dual invariant and absolute properties of relations. Rozprawy Matematyczne (Dissertationes Mathematicae) XXIX (1962) pp 1–38.
L’espace des modeles d’une theorie formalisee et quelquesunes des applications. Annales de la Faculte des Sciences de L’Universite Clevmant 7 (1962) pp 107–116.
The Hilbert epsilon function in many valued logics. Acta Phil. Fennica 16 (1963) pp 169–188.
Mostowski (+ M. Stark) Introduction to Higher Algebra. Oxford Warszawa 1963 pp 474.
Widerspruchsfreiheit und Unabhangigkeit der Kontinuumhypothese. Elemente der Mathematik 19 (1964) pp 121–125.
Thirty years of foundational studies Acta Phil. Fennica 17 (1965) pp 1–180.
Models of Zermelo-Fraenkel set-theory satisfying the axiom of constructibility. Acta Phil. Fennica 18 (1965) pp 135–144.
(+ K. Kuratowski) Teoria Mnogości. wyd. II (całkowicie zmienione). Monografie Matematyczne XXVII Warszawa 1966 pp 1–375.
Mostowski Modeles transitifs de le theorie des ensembles de Zermelo—Fraenkel. Univ. de Montreal 1967 pp 170.
Mostowski Recent results in set theory. in: Problems in the philosophy of mathematics, Studies in Logic and the Foundations of Mathematics Amsterdam 1967 pp 82–96 i 105–108.
O niektórych nowych wynikach matematycznych dotyczących teorii mnogości. Studia Logica 20 (1967) pp 99–116.
Mostowski Tarski Alfred. in: The Encyclopedia of Philosophy, ed. by Paul Edwards New York 1967 Vol. 8 pp 77–81.
Mostowski (+ K. Kuratowski) Set theory. (translated from polish) Amsterdam Warszawa 1967 pp 417 Studies in Logic and the Foundations of Mathematics.
Mostowski Craig interpolation theorem in some extended systems of logic. in: Logic, Methodology and Philosophy of Science III Studies in Logic and the Foundations of Mathematics Amsterdam 1968 pp 87–103.
Mostowski Models of Set Theory. C.I.M.E. (Italy), 1968. (Lectures delivered in Varenna September 1968) pp 67–179.
Niesprzeczność i niezależność hipotezy continuum. Wiadomości Matematyczne 10 (1968) pp 175–182.
(+ Y. Suzuki) On ω-models which are not β-models. Fundamenta Mathematicae LXV (1969) pp 83–93.
Mostowski Constructible sets with applications. Studies in Logic and Foundations of Mathematics Amsterdam 1969 pp 1–269.
Mostowski (+ K. Kuratowski) Teorija mnozestv. Moskva 1970 pp 416.
Models of second order arithmetic with definable Skolem functions. Fundamenta Mathematicae LXXV (1972) pp 223–234.+Correction ibid Models of second order arithmetic with definable Skolem functions. Fundamenta Mathematicae LXXXIV (1974) p 173.
A transfinite sequence of ω-models. Journal of Symbolic Logic 37 (1972) pp 96–102.
Mostowski Sets. in: Scientific thought, Paris-Hague 1972 pp 1–34.
Matematyka a logika. Refleksje przy lekturze książki A. Grzegorczyka “Zarys arytmetyki teoretycznej” wraz z próbą recenzji. Wiadomości Matematyczne 15 (1972) pp 79–89.
Mostowski Partial ordering of the family of ω-models. Logic Methodology and Philosophy of Science IV. Studies in Logic and the Foundation of Mathematics Amsterdam 1973 pp 13–28.
Mostowski A contribution to teratology. Izbrannye voprosy algebry i logiki Nowosybirsk 1973 pp 184–196.
Mostowski Konstruktivnye mnozestva i ich prilozenije. Moskva 1973 (translated from English) pp 256.
Some Problems in the Axiomatic Theory of Clases. Bolletin U.M.I. 9 (1974) pp 161–170.
Observations concerning elementary extensions of ω-models I. Proceedings of AMS Symposia in Pure Mathematics 25 (1975) pp 349–355.
Mostowski An exposition of forcing. in: Algebra and Logic, Springer Lecture Notes 450 (1975) pp 220–282.
Mostowski (+ W. Marek) On extendability of the models of ZF set theory to the models of KM theory of classes. in: Springer Lecture Notes 499, Proc. of the 1974 Kiel conference pp 460–542.
Mostowski A remark on models of the Gödel-Bernays axioms for set-theory. Preprint Uniwersytetu Warszawskiego 1974 (to appear in the Bernays volume).
Travaux de W. Sierpiński sur la theoriedes ensembles et ses applications. La theorie generale des ensembles. Introduction to: Wacław Sierpiński, Oeuvres choisies, vol. II Warszawa 1975 pp 9–13.
Mostowski (+ K. Kuratowski) Set theory. (revised edition). Studies in Logic and the Foundations of Mathematics Amsterdam Warszawa (w druku).
Mostowski Refleksje na temat pewnego wykładu z historii matematyki. O nauczaniu historii nauki, pp 231–243.
Mostowski Two remarks on the models of Morse’ set theory. (This proceedings).
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Marek, W., Srebrny, M., Zarach, A. (1976). Curriculum vitae of A. Mostowski. In: Marek, W., Srebrny, M., Zarach, A. (eds) Set Theory and Hierarchy Theory A Memorial Tribute to Andrzej Mostowski. Lecture Notes in Mathematics, vol 537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096888
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