Timeline for Is this set theory equivalent to ZFC?
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| Jan 2, 2021 at 21:18 | history | edited | Vladimir Reshetnikov | CC BY-SA 4.0 |
[Edit removed during grace period]
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| Dec 31, 2020 at 16:13 | history | edited | Vladimir Reshetnikov | CC BY-SA 4.0 |
typesetting
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| Dec 31, 2020 at 16:11 | vote | accept | Vladimir Reshetnikov | ||
| Dec 30, 2020 at 18:46 | history | edited | Vladimir Reshetnikov | CC BY-SA 4.0 |
Rephrasing of some definitions, and improved typesetting
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| Dec 30, 2020 at 18:14 | history | edited | Vladimir Reshetnikov | CC BY-SA 4.0 |
Better typesetting and coloring of formulae
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| Dec 30, 2020 at 18:07 | comment | added | Vladimir Reshetnikov | @dodd Sorry, I inadvertently dropped 2 quantifiers $\forall s\,\exists w$ when I typed the last formula. $s$ is any set, and $w$ is a superset of its transitive closure under $\prec$ relation, and the whole formula says $w$ exists for any $s$, provided that $\prec$ is set-like. Thanks for the correction, I fixed the formula. | |
| Dec 30, 2020 at 18:03 | history | edited | Vladimir Reshetnikov | CC BY-SA 4.0 |
Add missing quantifiers
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| S Dec 30, 2020 at 9:49 | history | suggested | gmvh |
Added top-level tag
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| Dec 30, 2020 at 9:21 | review | Suggested edits | |||
| S Dec 30, 2020 at 9:49 | |||||
| Dec 30, 2020 at 7:31 | history | became hot network question | |||
| Dec 30, 2020 at 6:06 | comment | added | markvs | If you believe that your axioms imply the axiom of infinity, you may want to present a proof here. Your last line of OP is not clear to me. What is $s$? | |
| Dec 30, 2020 at 2:33 | comment | added | Vladimir Reshetnikov | @dodd Sorry, I made some significant corrections and clarifications to my question. Do you make the same claim about the corrected version? | |
| Dec 30, 2020 at 2:28 | history | edited | Vladimir Reshetnikov | CC BY-SA 4.0 |
deleted 6 characters in body
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| Dec 30, 2020 at 2:21 | comment | added | Vladimir Reshetnikov | @HanulJeon The Replacement says that if we replace each element of a set by exactly one object, then the result is still a set. This "bolder" version asserts that we can replace an element not only by a single object, but by all elements of any set, and even if such replacement is repeated transitively, we still have a set at the end. | |
| Dec 30, 2020 at 2:16 | comment | added | Vladimir Reshetnikov | @PaceNielsen I updated my question to express my idea more clearly. There is a proposed formalization for the transitive closure not using a notion of an infinite set or a union. I believe, the last axiom is strong enough to imply Axioms of Infinity and Union. | |
| Dec 30, 2020 at 2:10 | history | edited | Vladimir Reshetnikov | CC BY-SA 4.0 |
The last axiom corrected and formalized
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| Dec 30, 2020 at 1:00 | answer | added | Elliot Glazer | timeline score: 12 | |
| Dec 30, 2020 at 0:34 | comment | added | markvs | The class consisting of all finite sets satisfies your axioms but not ZFC. | |
| Dec 29, 2020 at 23:53 | comment | added | Hanul Jeon | Could you explain why your last axiom schema is a bolder version of Replacement? | |
| Dec 29, 2020 at 23:39 | comment | added | Pace Nielsen | How are you defining the transitive closure of a relation without the axiom of infinity? | |
| Dec 29, 2020 at 23:39 | comment | added | Vladimir Reshetnikov | The last axiom schema can be thought of as a bolder version of Replacement. | |
| Dec 29, 2020 at 23:25 | history | asked | Vladimir Reshetnikov | CC BY-SA 4.0 |