Timeline for Can the axiom of choice be proved with ZF+Tarski axiom?
Current License: CC BY-SA 4.0
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| Nov 26 at 6:39 | comment | added | user76284 | Your reference shows that $\mathsf{A}_2 \to \mathsf{Choice}$. But how does $\mathsf{TA} \to \mathsf{A}_2$? | |
| Jan 10, 2023 at 21:42 | vote | accept | Carlos Freites | ||
| Jan 10, 2023 at 21:42 | comment | added | Carlos Freites | Interesting, it is very powerful: "It is Tarski's axiom that distinguishes TG from other axiomatic set theories. Tarski's axiom also implies the axioms of infinity, choice,[1][2] and power set.[3][4] It also implies the existence of inaccessible cardinals, thanks to which the ontology of TG is much richer than that of conventional set theories such as ZFC. " Then the other natural question would be why ZFC is much more popular than the Tarski-Grothendieck. I conjecture GT must have more contra intuitive results than for example the ZFC Banach Tarski paradox. | |
| Jan 9, 2023 at 14:23 | history | answered | Alex M. | CC BY-SA 4.0 |