Generic extensions of models of ZFC
Commentationes Mathematicae Universitatis Carolinae (2017)
- Volume: 58, Issue: 3, page 347-358
- ISSN: 0010-2628
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topBukovský, Lev. "Generic extensions of models of ZFC." Commentationes Mathematicae Universitatis Carolinae 58.3 (2017): 347-358. <http://eudml.org/doc/294135>.
@article{Bukovský2017,
abstract = {The paper contains a self-contained alternative proof of my Theorem in Characterization of generic extensions of models of set theory, Fund. Math. 83 (1973), 35–46, saying that for models $M\subseteq N$ of ZFC with same ordinals, the condition $Apr_\{M,N\}(\kappa )$ implies that $N$ is a $\kappa $-C.C. generic extension of $M$.},
author = {Bukovský, Lev},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {inner model; extension of an inner model; $\kappa $-generic extension; $\kappa $-C.C. generic extension; $\kappa $-boundedness condition; $\kappa $ approximation condition; Boolean ultrapower; Boolean valued model},
language = {eng},
number = {3},
pages = {347-358},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Generic extensions of models of ZFC},
url = {http://eudml.org/doc/294135},
volume = {58},
year = {2017},
}
TY - JOUR
AU - Bukovský, Lev
TI - Generic extensions of models of ZFC
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 3
SP - 347
EP - 358
AB - The paper contains a self-contained alternative proof of my Theorem in Characterization of generic extensions of models of set theory, Fund. Math. 83 (1973), 35–46, saying that for models $M\subseteq N$ of ZFC with same ordinals, the condition $Apr_{M,N}(\kappa )$ implies that $N$ is a $\kappa $-C.C. generic extension of $M$.
LA - eng
KW - inner model; extension of an inner model; $\kappa $-generic extension; $\kappa $-C.C. generic extension; $\kappa $-boundedness condition; $\kappa $ approximation condition; Boolean ultrapower; Boolean valued model
UR - http://eudml.org/doc/294135
ER -
References
top- Balcar B., A theorem on supports in the theory of semisets, Comment. Math. Univ. Carolin. 14 (1973), 1–6. Zbl0281.02060MR0340015
- Balcar B., Štěpánek P., Teorie množin, (Set Theory, Czech), Academia, Prague, 1986, second edition 2003. Zbl0635.03039MR0911270
- Bukovský L., Ensembles génériques d'entiers, C.R. Acad. Sci. Paris 273 (1971), 753–755. Zbl0231.02086MR0286647
- Bukovský L., 10.4064/fm-83-1-35-46, Fund. Math. 83 (1973), 35–46. Zbl0344.02043MR0332477DOI10.4064/fm-83-1-35-46
- Friedman S.D., Fuchino S., Sakai H., On the set-generic multiverse, preprint.
- Gaifman H., 10.2140/pjm.1964.14.61, Pacific J. Math. 14 (1964), 61–73. Zbl0127.02306MR0161952DOI10.2140/pjm.1964.14.61
- Jech T., Set Theory, the third millenium edition, revised and expanded, Springer, Berlin, 2003. Zbl1007.03002MR1940513
- Kunen K., Set Theory, Studies in Logic 34, College Publications, London, 2013. Zbl0960.03033MR2905394
- Laver R., 10.1016/j.apal.2007.07.002, Ann. Pure Appl. Logic 149 (2007), 1–6. Zbl1128.03046MR2364192DOI10.1016/j.apal.2007.07.002
- Solovay R., 10.2307/1970696, Ann. of Math. 92 (1970), 1–56. Zbl0207.00905MR0265151DOI10.2307/1970696
- Vopěnka P., General theory of -models, Comment. Math. Univ. Carolin. 8 (1967), 145–170. Zbl0162.01701MR0214460
- Vopěnka P., Balcar B., On complete models of the set theory, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 15 (1967), 839–841. Zbl0177.01404MR0242659
- Vopěnka P., Hájek P., The Theory of Semisets, Academia, Prague, 1972. Zbl0332.02064MR0444473
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