A good introduction to axiomatic set theory

Asked Apr 07 '19 at 14:50

Active Apr 08 '19 at 01:59

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I'm doing my undergraduate dissertation on axiomatic set theory, and i'm using Jean-Louis Krivine's book "Theorie des ensembles" as a reference book. My dissertation focuses only on the first two chapters " zermelo fraenkel set theory " and " cardinals and ordinals ". And i'm searhing for some references to help me write the introduction to my dissertation.

Any help would be much appreciated.

edited Apr 08 '19 at 01:59

Andrés E. Caicedo

81,687

asked Apr 07 '19 at 14:50

Matsukazi Issy

3

Suppes' Axiomatic Set Theory and Derek Goldrei, Classic set theory, Chapman & Hall (1996) – Mauro ALLEGRANZA Apr 07 '19 at 14:55
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I like Both Enderton's book Set theory and Jech's book Set theory 3rd millennium edition. Have a look at them because maybe they are not exactly what you are looking for. – Dog_69 Apr 07 '19 at 15:15
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For a historical treatment of the development of $\mathsf{ZFC}$, I would recommend "The Philosophy Of Set Theory" by Mary Tiles – Not Mike Apr 07 '19 at 15:53
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You might find this small note useful. – Asaf Karagila Apr 07 '19 at 17:18
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See Textbooks on set theory. – Dave L. Renfro Apr 07 '19 at 17:20
@AsafKaragila This is not related to my question here but to an answer you gave here [link] (https://math.stackexchange.com/questions/916072/what-axioms-does-zf-have-exactly)
I hope i'm not violating any terms by asking here, i just don't have reputation points enough to reply to your answer there. There you gave your preffered list of axioms for zermelo fraenkel set theory which contained the axiom of regularity; but in Jean-Louis Krivine's book "Theorie des ensembles" he used the same set of axioms but excluding the axiom of regularity, so can we prove it from the other axioms?
– Matsukazi Issy Apr 08 '19 at 12:50
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No, we cannot prove Regularity from the other axioms of ZF. – Asaf Karagila Apr 08 '19 at 12:51
@AsafKaragila humm i see, thanks for answering, i wonder then why it wasn't used in the book.. – Matsukazi Issy Apr 08 '19 at 12:57

A good introduction to axiomatic set theory

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