Metamathematics of the alternative set theory. I.
Commentationes Mathematicae Universitatis Carolinae (1979)
- Volume: 020, Issue: 4, page 697-722
- ISSN: 0010-2628
Access Full Article
topHow to cite
topSochor, Antonín. "Metamathematics of the alternative set theory. I.." Commentationes Mathematicae Universitatis Carolinae 020.4 (1979): 697-722. <http://eudml.org/doc/17003>.
@article{Sochor1979,
author = {Sochor, Antonín},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {alternative set theory; formal system; Kelley-Morse set theory; formalization of metamathematics},
language = {eng},
number = {4},
pages = {697-722},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Metamathematics of the alternative set theory. I.},
url = {http://eudml.org/doc/17003},
volume = {020},
year = {1979},
}
TY - JOUR
AU - Sochor, Antonín
TI - Metamathematics of the alternative set theory. I.
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1979
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 020
IS - 4
SP - 697
EP - 722
LA - eng
KW - alternative set theory; formal system; Kelley-Morse set theory; formalization of metamathematics
UR - http://eudml.org/doc/17003
ER -
References
top- P. BERNAYS, A system of axiomatic set theory, Journ. Symb. Logic 2 (1937), 65-77. (1937) Zbl0019.29403
- J. L. BELL A. B. SLOMSON, Models and Ultraproducts, North-Holland 1971. (1971)
- R. BOYD G. HENSEL H. PUTNAM, A recursion-theoretic characterization of the ramified analytic hierarchy, T.A.M.S. 141 (1969), 37-62. (1969) MR0242673
- H. ENDERTON, Constructible -models, Zeitschrift f. math. Logik 19 (1973), 277-282. (1973) Zbl0301.02053MR0325376
- P. COHEN, The independence of the continuum hypothesis, Proc. Nat. Acad. Sci. 50 (1963), 1143-1148 and 51 (1964), 105-110. (1963) MR0157890
- K. GÖDEL, The consistency of the axiom of choice and of the generalized continuum hypothesis, Ann. of Math. Studies, Princeton 1940. (1940)
- S. FEFERMAN, Arithmetization of metamathematics in a general setting, Fundamenta Math. 49 (1960-61), 35-92. (1960) Zbl0095.24301MR0147397
- A. HAJNAL, On a Consistency Theorem Connected with the Generalized Continuum Problem, Zeitschrift f. math. Logik 2 (1956), 131-136. (1956) Zbl0074.01203MR0091914
- R. MONTAGUE, Semantical closure ani non-finite axiomatizability I in Infinistic methods, Warsaw 1959, 45-69. (1959) MR0150033
- A. MOSTOWSKI, On models of axiomatic systems, Fund. Math. 39 (1952), 133-158. (1952) MR0054547
- M. MACHOVER J. HIRSCHFELD, Lectures on Non-Standard Analysis, Lect. Notes in Math, no 94, Springer 1969. (1969) MR0249285
- W. MAREK A. SOGHOR, On weak Kelley-Morse theory of classes, Comment. Math. Univ. Carolinae 19 (1978), 371-381. (1978) MR0491176
- W. MAREK M. STREBRNY, No minimal transitive model of , Zeitschr. f. math. Logik 21 (1975), 225-228. (1975) MR0381996
- I. L. NOVAK, Models of consistent systems, Fund. Math. 37 (1950), 87-110. (1950) Zbl0039.24504MR0041082
- L. RIEGER, A contribution to Gödel's axiomatic set theory III, Czech. Math. J. 9 (1959), 51-88. (1959)
- A. ROBINSON, Non-Standard Analysis, North-Holland, Amsterdam 1966. (1966) Zbl0151.00803MR0205854
- J. R. SHOENFIELD, Mathematical Logic, Reading, Mass. 1968. (1968) MR0225631
- J. R. SHOENFIELD, A relative consistency proof, JSL 19 (1954), 21-28. (1954) Zbl0055.00404MR0060433
- T. SKOLEM, Einige Bemerkung zur axiomatischen Begründung der Mengenlehre, Wissenschaftl. Vorträge gen. a. d. V. Kongress d. Skandinavischer Mathematiker, Helsingfors 1923, 217-232. (1923)
- A. SOCHOR, The alternative set theory, Set theory and hierarchy theory - A Memorial tribute to A. Mostowski, Lect. Notes in Math, no 537, 259-271, Springer 1976. (1976) Zbl0344.02049MR0462948
- A. SOCHOR, Differential calculus in alternative set theory, Set theory and hierarchy theory V, Lect. Notes in Math, no 619, 273-284, Springer 1977. (1977) MR0472524
- A. SOCHOR, Real classes in the ultrapower of hereditarily finite sets, Comment. Math. Univ. Carolinae 16 (1975), 637-640. (1975) Zbl0327.02047MR0389588
- A. SOCHOR P. VOPĚNKA, Endomorphic universes and their standard extensions, Comment. Math. Univ. Carolinae 20 (1979), 605-629. (1979) MR0555178
- A. SOCHOR P. VOPĚNKA, Revealments, to appear in Comment. Math. Univ. Carolinae 21 (1980). (1980) MR0566243
- A. TARSKI A. MOSTOWSKI A. ROBINSON, Undecidable Theories, North-Holland 1953. (1953) MR0058532
- P. VOPĚNKA, Mathematics in Alternative Set Theory, Teubner-Texte, Leipzig 1979. (1979) MR0581368
- P. VOPĚNKA P. HÁJEK, The Theory of Semisets, North-Holland Amsterdam and Academia Prague 1972. (1972) MR0444473
- P. ZBIERSKI, Models for higfter order arithmetic, BAPS 19 (1971), 557-562. (1971) MR0307907
Citations in EuDML Documents
top- Jiří Sgall, Construction of the class FN
- Antonín Sochor, Metamathematics of the alternative set theory. II.
- Michal Resl, On models in the alternative set theory
- Nando Prati, Alternative set theory with elementary classes
- Jiří Sgall, Forcing in the alternative set theory. I
- Antonín Sochor, Petr Vopěnka, The axiom of reflection
- Michal Resl, Antonín Sochor, Provability in the alternative set theory
- Karel Čuda, The consistency of the measurability of projective semisets
- Antonín Sochor, Petr Vopěnka, Shiftings of the horizon
- Karel Čuda, Blanka Vojtášková, Model-theoretical constructions in AST. I.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.