A Note on Intended and Standard Models

1. Awodey, S., and E. H. Reck. Completeness and categoricity. Part I: Nineteenth-century axiomatics to twentieth-century metalogic, History and Philosophy of Logic 23, 2002, pp. 1-30.10.1080/01445340210146889Search in Google Scholar

2. Bedürftig, T., and R. Murawski. Philosophy of mathematics, Berlin Boston: Walter de Gruyter GmbH, 2018.10.1515/9783110468335Search in Google Scholar

3. Borsuk, K., and W. Szmielew. Podstawy geometrii, Warszawa: Państwowe Wydawnictwo Naukowe, 1975.Search in Google Scholar

4. Carnap, R., and F. Bachmann. Über Extremalaxiome, Erkenntnis 6, 1936, pp. 166-188.10.1007/BF02538231Search in Google Scholar

5. Carnap, R., and F. Bachmann. On extremal axioms [English translation of Carnap and Bachmann 1936, by H.G. Bohnert], History and Philosophy of Logic 2, 1981, pp. 67-85.10.1080/01445348108837022Search in Google Scholar

6. Corcoran, J. Categoricity, History and Philosophy of Logic 1, 1980, pp. 187-207.10.1080/01445348008837010Search in Google Scholar

7. Corcoran, J. From categoricity to completeness, History and Philosophy of Logic 2, 1981, pp. 113-119.10.1080/01445348108837024Search in Google Scholar

8. Feferman, S. Conceptions of the continuum, Intellectica 51, 2009, pp. 169-189.10.3406/intel.2009.1737Search in Google Scholar

9. Fraenkel, A. A. Einleitung in die Mengenlehre, Berlin: Verlag von Julius Springer, Berlin, 1928.10.1007/978-3-662-42029-4Search in Google Scholar

10. Fraenkel, A. A., Y. Bar-Hillel, and A. Levy. Foundations of set theory, Amsterdam London: North-Holland Publishing Company, 1973.Search in Google Scholar

11. Gaifman, H. Nonstandard models in a broader perspective, In A. Enayat and R. Kossak (eds.), Nonstandard models in arithmetic and set theory. AMS Special Session Nonstandard Models of Arithmetic and Set Theory, January 15–16, 2003, Baltimore, Maryland. Contemporary Mathematics 361, Providence, Rhode Island: American Mathematical Society, 2004, pp. 1-22.10.1090/conm/361/06585Search in Google Scholar

12. Grzegorczyk, A. On the concept of categoricity, Studia Logica 13, 1962, pp. 39-66.10.1007/BF02317255Search in Google Scholar

13. Hilbert, D. Grundlagen der Geometrie, Festschrift zur Feier der Enthüllung des Gauss-Weber-Denkmals in Göttingen, Leipzig: Teubner, 1899.Search in Google Scholar

14. Hodges, W. Model theory, Cambridge: Cambridge University Press, 1993.Search in Google Scholar

15. Lindenbaum, A., and A. Tarski. Über die Beschränkheit der Ausdruckmittel deduktiver Theorien, Ergebnisse eines mathematischen Kolloquiums 1934–1935, 7, 1936, pp. 15-22.Search in Google Scholar

16. Mancosu, P. The adventure of reason. Interplay between philosophy and mathematical logic, 1900–1940, Oxford: Oxford University Press, 2010.Search in Google Scholar

17. Marker, D. Model theory: an introduction, New York Berlin Heidelberg: Springer-Verlag, 2002.Search in Google Scholar

18. Murawski, R. Funkcje rekurencyjne i elementy metamatematyki. Problemy zupełności, rozstrzygalności, twierdzenia Gödla, Poznań: Wydawnictwo Naukowe UAM, 2000.Search in Google Scholar

19. Pogonowski, J. Extremal axioms. Logical, mathematical and cognitive aspects, Poznań: Wydawnictwo Nauk Społecznych i Humanistycznych UAM, 2019.Search in Google Scholar

20. Putnam, H. Models and reality, The Journal of Symbolic Logic 45, 1980, pp. 464-482.10.2307/2273415Search in Google Scholar

21. Schiemer, G. Carnap on extremal axioms, ‘completeness of models’, and categoricity, The Review of Symbolic Logic 5 (4), 2012, pp. 613-641.10.1017/S1755020312000172Search in Google Scholar

22. Tarski, A. On the completeness and categoricity of deductive theories. Appendix in Mancosu, P. The adventure of reason. Interplay between philosophy and mathematical logic, 1900–1940, Oxford: Oxford University Press, 2010, 1940, pp. 485-492.Search in Google Scholar

23. Woleński, J. Metamatematyka a epistemologia, Warszawa: Wydawnictwo Naukowe PWN, 1993.Search in Google Scholar

24. Woleński, J. Kwadrat logiczny – uogólnienia, interpretacje, In J. Perzanowski and A. Pietruszczak (eds.), Logika & filozofia logiczna, Toruń: Wydawnictwo Uniwersytetu Mikołaja Kopernika, 2000, pp. 45-57.Search in Google Scholar

25. Woleński, J. Epistemologia. Poznanie, prawda, wiedza, realizm, Warszawa: Wydawnictwo Naukowe PWN, 2005.Search in Google Scholar

26. Zermelo, E. Über Grenzzahlen und Mengenbereiche: Neue Untersuchungen über die Grundlagen der Mengenlehre, Fundamenta Mathematicae 16, 1930, pp. 29-47.10.4064/fm-16-1-29-47Search in Google Scholar