Timeline for Are there fragments of set theory which are axiomatized with only bounded (restricted) quantifiers used in axioms?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 18, 2014 at 20:45 | answer | added | Goldstern | timeline score: 4 | |
| Aug 18, 2014 at 19:54 | answer | added | Joel David Hamkins | timeline score: 6 | |
| Aug 18, 2014 at 2:06 | comment | added | Ioachim Drugus | @Goldstern, I am not sure how the constants in the language of a set theory correlate with whether there is an axiomatization with bounded quantifiers only, of the set theory or of a fragment of it - probably, I am missing something. Also, I am not interested in a set theory of hereditarily finite sets (I don't know how you figured out those links are about such sets - those which I access don't mention hereditarily finite sets). But ZF (with infinitary axiom), NBG, or even Generalized Set Theory of Boolos, are good for this question. | |
| Aug 18, 2014 at 1:42 | comment | added | Ioachim Drugus | Really, there is no clash of two terms - thanks. But since many authors use the term "restricted quantifier" I would prefer it. | |
| Aug 17, 2014 at 22:24 | comment | added | Emil Jeřábek | Occurrences of variables that are not free are bound rather than bounded, so this doesn’t clash with the standard term “bounded quantifier”. | |
| Aug 17, 2014 at 21:54 | comment | added | Goldstern | The tag "set theory" indicates to me that you might be interested in a theory that includes a version of the axiom of infinity. But the references in the wikipedia article seem to deal with computations with hereditarily finite sets only. | |
| Aug 17, 2014 at 21:48 | comment | added | Goldstern | What language are you thinking of? ZF is often written in a purely relational language (with no constant symbols), so there won't be any closed formulas in which all quantifiers are bounded. It seems to me you need at least the constant $\omega$. Which function symbols do you want to allow? Power set? Smallest your favorite cardinal above $\alpha$? | |
| Aug 17, 2014 at 16:52 | history | asked | Ioachim Drugus | CC BY-SA 3.0 |